Cole has fallen behind Cesar Azpilicueta in the pecking order and hasn't started a Premier League game since 11 January.
The Chelsea manager called the Arsenal boss a "specialist in failure". The feud escalated by Wenger calling Mourinho an "embarrassment".
The January transfer window closed at 11pm on Friday evening. Here is a round-up of what happened where in London
Jose Mourinho has branded Arsene Wenger a "specialist in failure" as he hit back at the Arsenal manager for suggesting the title was "Chelsea's to lose".
"He is a specialist in failure. I'm not. So if supposing he's right and I'm afraid of failure, it's because I don't fail many times. So maybe he's right. I'm not used to failing," the Chelsea manager said.
"But the reality is he's a specialist because, eight years without a piece of silverware, that's failure. If I did that in Chelsea I'd leave London and not come back."
Chelsea currently top the Premier League table sitting just one point above Arsenal.
Jose Mourinho says a pep talk given to Chelsea players by the team's masseur Billy McCulloch helped power the team to victory over Manchester City. McCulloch joined the club in 2001 and provides a constant source of entertainment behind the scenes at Stamford Bridge.
Jose Mourinho said: "I didn't speak. It was Billy the masseur. He was screaming, so much I didn't understand him. The players were clapping - okay, let's go. It was Billy's team talk. The last time I spoke to the players was at midday.
"I'm serious, Billy was fantastic. I didn't understand [his accent] but it looks like the players understood."
Jose Mourinho insists Arsenal are the favourites to win the title race as his side sits third behind Manchester City.
Despite ending City's 100 per cent home league record, and becoming the first side since Birmingham in November 2010 to prevent City scoring at home in the Premier League, the Chelsea boss still sees his side as the outsiders:
A victory is a victory but a victory against a very good team is better than a victory against an ordinary team. More credit to my players.
We love the big games. Obviously when you love it maybe you feel extra motivated for that and I keep saying, the best thing for the evolution of this team is not to play Europa League, not to be 15-20 points behind the leader but with pressure to be there, to be close to the leaders.
Maybe Arsenal deserve it more than us. They are top of the league and they are the favourites. We go behind them and play and watch.
The Chelsea boss' assessment of the title race was typically Mourinho.
– Jose Mourinho, Chelsea manager
Two horses and a little horse that still needs milk and to learn how to jump. A horse that next season can race.
We are a team in evolution but this is the kind of performance that helps the team to grow up a lot, tactically, mentally, I think it was fantastic.
Chelsea beat Manchester City tonight in a top of the table clash at the Etihad Stadium. Branislav Ivanovic's goal ended City's chance to be top of the Premier League.
Samuel Eto'o, Nemanja Matic and Gary Cahill all hit the woodwork as Chelsea looked the better team throughout.
In my time we were accused of buying the title, no? Because our owner was Mr Abramovich, just arrived in the country. Maybe now people see City in a different way.
Times change. Maybe 10 years ago a huge investment in the club was something that people hated and in this moment it's something people accept in a different way.
– Jose Mourinho, Chelsea manager
Probably, if UEFA goes with Financial Fair Play until the last consequence and they explain really to the people what Financial Fair Play means, maybe in that moment people will realise that some teams are different to other teams.
But it's something I don't think about at this moment.
Chelsea manager Jose Mourinho says it will be "impossible" for clubs to compete with Manchester City, if Financial Fair Play is not enforced.
Financial Fair Play rules were introduced to stop football clubs spending more than they earn.
City's vast spending in an era of Financial Fair Play has come in for repeated criticism from Mourinho - he wants to see the economic regulations are enforced by European football's governing body UEFA. Jose Mourinho said:
"If they (football's authorities) want to make it impossible (to compete with City), it's impossible. (Chelsea) are not competing outside what is important for us, the 'fair' Financial Fair Play.
"We are working, thinking and believing that Financial Fair Play is going to be in practice. So there are things that are impossible for us (to do)."
Former Chelsea, Liverpool and Aston Villa striker Tony Hateley has died at the age of 72.
Hateley scored 211 league goals during his career and was a club-record signing for both Chelsea and Liverpool, costing the Blues £100,000 in 1966.
Gary Cahill says Chelsea face the "ultimate challenge" when travelling to Premier League leaders Manchester City on Monday.
Chelsea on Wednesday night recorded a seventh clean sheet in nine games in all competitions in a goalless draw with West Ham which left Jose Mourinho so frustrated he described Sam Allardyce's tactics as from the 19th century.
City boast a 100 per cent record from 11 home games, scoring 42 goals in the process.
Gary Cahill told Chelsea TV: "They're banging goals in left, right and centre. It's going to be really tough. We had a really good result against them at home; away from home (at the Etihad Stadium) they've been so, so strong.
"I suppose it's the ultimate test. It's going to be a really, really tough game. We've got to try to look forward to those games and going there on Monday is exciting."