Hearts are expected to return with an improved offer for Northern Ireland and Burton striker Liam Boyce.
The 28-year-old's contract with the Championship side is due to expire this summer and the club are understood to be willing to do business only if an acceptable offer comes in.
So far, that has not been the case as the Brewers have knocked back bids from both the Edinburgh club and Sunderland.
The Black Cats had been expected to continue their chase even after signing Boyce's international team-mate Kyle Lafferty.
However, manager Phil Parkinson has now poured cold water on the idea.
“Liam is a player I’ve known for a while and we’ve watched recently,” he said.
“With Lafferty coming in, and Charlie (Wyke) and (Will) Grigg at the top end of the pitch, to bring another (striker) would I think be one too many.”
There had been speculation that Northern Ireland forward Grigg could drop to League Two, possibly Salford City, to make room in the Sunderland squad but Parkinson also said he is reluctant to let any of his current forward options depart.
That could all leave the path clear for Hearts to sign Boyce, if they put enough capital forward.
The Jam Tarts are currently four points adrift at the foot of the Scottish Premiership table and are desperate for some added firepower to shoot their way to survival.
Boyce certainly fits that bill, having won the division's golden boot in his last season with Ross County before moving to Burton in 2017.