Nigel Farage has visited Cardiff Bay to meet a number of assembly members who have defected to the Brexit Party.
ITV Wales' Political Editor Adrian Masters said Reckless will be the likely leader of the group in the Welsh Assembly.
Former UKIP members Mandy Jones, Caroline Jones and David Rowlands, who announced he would be leaving UKIP earlier in the day, along with Reckless, have formally requested to be recognised in the Welsh Assembly.
Mr Rowlands' departure means that UKIP will lose its status as an Assembly group, with guaranteed slots for questions and debates in the Senedd and places on committees.
UKIP's leader in the Assembly Gareth Bennett said he is "sorry and disappointed" at Mr Rowlands' decision.
I am sorry and disappointed that David has decided to take this step. David was elected under a UKIP mandate. His departure from the group will inevitably lead to job losses for our hard working support staff, something which David was well aware of before reaching his decision.
The Brexit Party's application to form a group will now be considered by the Assembly's Presiding Officer or Llywydd, Elin Jones. There's some resistance in the Senedd to the idea.
Plaid Cymru said the application to form the group should not be allowed - saying the Senedd is "not a playground for Brexiteer chancers".
The Brexit Party did not stand and were not elected in the 2016 elections.
Labour claimed that the new group, if it's recognised, would stand for nothing more than its own short-term, narrow self-interest.
This so-called new political group has no democratic mandate in Wales. It has not won a single vote in an Assembly election, let alone a seat in the National Assembly. We are on the brink of seeing four politicians – each of whom has played musical chairs with their own and other political groups in the Senedd – joining the Brexit Party to lend it a political credibility it has not earned through the ballot box.