It has not been decided whether the brief, which may include a City element due to TSB's intention to list on the stockmarket, will be handed to one agency or split.
Next year's initial public offering is expected to value the bank, which has five million customers, at around £1.5bn to £2bn.
A spokeswoman for TSB confirmed the talks, stating: "We have reached out to a number of agencies. We’re at the very early stages but the remit will cover corporate comms, also overseeing media and public affairs work."
TSB launched as a distinct bank from Lloyds this autumn after the European Commission forced Lloyds Banking Group to carve out the business as a penalty for taking a £20bn government bailout in the 2008 financial crisis.
It has already been active in the political space under head of public affairs Anthony Thompson, including taking a small exhibition stand at the Conservative Party Conference two months ago.
It is bulking up its comms team and yesterday announced the hire of Virgin’s Nigel Gilbert for the newly created role of brand, customer and comms director.
TSB has launched with the slogan "Welcome back to local banking", but one corporate PR figure warned that an incoming agency would have to work hard to differentiate the bank in a tarnished industry.
"Everyone has been tainted by what has gone before and it’s a tough market with a hugely cynical audience," they added.
"To gain trust TSB will have to back up its words by truly providing a more personal service. Comms will have to work very hard in defining what a local bank means in terms of its values and behaviour and investors will look just as hard at this as consumers."