BLM's digital division, Quantum, already holds the chain's digital planning and buying account.
TK Maxx heavily favours traditional media for its advertising, with the bulk of its budget going to television.
In the past 12 months, the company spent just £6,000 on online display media, compared with £5m for TV and £835,000 for press.
The direct marketing budget is £360,000 and the outdoor spend is £106,000, with small allocations to cinema and radio.
It is understood that eight agencies were invited to the initial chemistry meetings, although some declined because of client conflict. All parties were required to sign non-disclosure agreements.
A spokeswoman for TK Maxx confirmed there were three agencies on the shortlist, but would not reveal who was involved.
She added that everyone involved had been notified.
BLM, MPG and MindShare declined to comment.