Richard Meddings is said to be in talks about joining the board of the bank as a non-executive director.
After taking on this role, he would then be expected to succeed the bank’s chairman, Will Samuel, next year, Sky News today reported.
TSB was spun out of Lloyds Banking Group four years ago as part of state aid rules from Brussels.
The bank delisted from the London Stock Exchange in 2015 as it was taken over by Spanish group Banco Sabadell.
Since leaving Standard Chartered, Meddings joined Deutsche Bank’s supervisory board in 2015.
He had previously joined the board of Legal and General Group in December 2014 before stepping down in May this year.