Talks will take place today, aimed at averting a tube strike next week.
Maintenance workers are due to stage a 72-hour strike on Tuesday from 4pm.
The dispute is over demands from the RMT union for all Tube Lines staff to get the same benefits as London Underground workers.
Tube Lines carries out upgrades and repairs on the Piccadilly, Northern and Jubilee Lines - and was bought by Transport for London two years ago.
Maintenance staff on three tube lines are entering their third day of strikes today.
A strike affecting the Jubilee, Northern and Piccadilly lines goes ahead from 4pm.
Union bosses have forecast "widespread" disruption, as workers who maintain and upgrade tube lines go on strike next week.