The Saddlers have already turned down one bid from the Scottish Championship club and are eager for the 23-year-old, who took his tally to the season to 10 by netting twice in Saturday’s 3-1 win at Port Vale, to sign a new deal at the Banks’s.
But another offer from Hearts looks increasingly likely with their manager, Robbie Neilson, claiming Adebayo has verbally agreed terms on a move to Tynecastle.
That prompted a statement from the Saddlers, insisting they have not agreed to sell the Fulham youth product.
Yet they are unable to prevent Adebayo, whose current deal expires in the summer, from discussing pre-contract terms with clubs from leagues outside England.
Under those same FIFA rules, the Saddlers would be due a fee of more than £100,000 should the striker join Hearts after his deal at the Banks's expires.
Neilson, meanwhile, defended his club’s conduct following criticism last week from Walsall boss Darrell Clarke.
He told the Edinburgh Evening News: “It's well documented we put an offer in for Adebayo. It initially got knocked back so we will see where that one goes and whether we go back in again.
“He has been the No.1 target for us for a while now. Ultimately, he is their player. He scored two goals again on Saturday. We just need to see if we can come to some agreement.
“I spoke to their manager (Clarke) on Friday night about it. The problem was that they didn't understand the rules, so I had to explain to them what the rules are when it's a cross-border transfer.
“They thought they were going by the English FA rules – that a player can only speak to other clubs when he enters the last month of his contract.
“The FIFA rules are that he can speak when he enters the last six months.”