Chelsea have received a verbal £40million bid for Gallagher from Spurs and have kept lines of communication open with their London rivals on Transfer Deadline Day.
The offer falls short of Chelsea’s nearly £50m asking price but all parties believe a deal could be struck in certain circumstances.
Tottenham need to sell Pierre-Emile Hojbjerg to Fulham to make any official bids but the Denmark international is currently reluctant to move to Craven Cottage.
His move could kick-start a chain reaction in the midfielder market with Joao Palhinha in talks about joining Bayern Munich before the German transfer window closes at 5pm BST.
Chalobah is also a target for Bayern, who are ready to waive through a loan move should Chelsea accept their offer.
There is no concern about his ongoing hamstring injuries and the only barrier remains Chelsea’s final decision to allow the defender to have a reunion with former manager Thomas Tuchel at the Allianz Arena.
Chelsea striker Mason Burstow has agreed a season-long loan move to Sunderland after making his first start for the Blues in the 2-1 win over AFC Wimbledon on Wednesday.
Defender Bashir Humphreys is also set for a Championship loan spell at Swansea.