The English League Two club are reluctant to let the 23-year-old leave, although his contract expires at the end of the season. Hearts want to strengthen their forward line before the January transfer window closes.
The Edinburgh club remain hopeful that a deal for Adebayo can materialise either now or in the summer when he becomes a free agent.
Asked about Adebayo at Thursday’s press conference, the Hearts manager Robbie Neilson said: “I don't want to speak about players contracted to other teams.
“We have a list of players we are looking to get in and we have a profile of the striker we are looking to bring into the club. We will continue to work on that.
“There are two or three targets we are pushing who fit the profile. Hopefully we can get it over the line. I said at the start [of the month] that I would like to get one in but it has to be the right one.
“I don’t to bring someone in who is just another number in the squad. We have to bring quality that is going to take the squad forward.”
Hearts increased their options in wide areas with the capture of the Scotland international winger Gary Mackay-Steven last week.
In addition to another forward, they also plan to sign a new midfielder this month after allowing Olly Lee to leave for Gillingham.