The Swede is one of seven first-team players out of contract at the end of the season but club management have already made it clear they want to keep him.
Discussions between Hearts officials and Sow’s agent have taken place as the Edinburgh club try to negotiate a longer deal for the 25-year-old. He has scored five goals in 14 appearances so far this term and is attracting interest from other teams.
Sow and his representatives will consider any contract offer from Tynecastle. Hearts head coach Robbie Neilson wants to secure the forward’s future before January - when Sow would be free to sign a pre-contract agreement with another club.
Also out of contract at Hearts next summer are goalkeepers Neil Alexander and Scott Gallacher, Polish defender Blazej Augustyn, Brazilian Igor Rossi, Spanish midfielder Miguel Pallardo and Dutchman Kenny Anderson. Belgian midfielder Arnaud Djoum is on a short-term deal which expires in January.
“We’ve made moves for the ones we want to talk to,” revealed Neilson. “Like anything in football, these things take time. We’ve spoken to Osman’s agent so we’re now just waiting to hear back again. I’d like to get it done.
“He’s proved so far this season that he can play in the Scottish Premiership.
“I’m hopeful we can get it tied up. The others will be dealt with in time. It all depends where they are, what their situation is in terms of age, appearances, what their future is with us and what we think.
“These things will probably be dealt with before January.
“The players are in good positions, they’re at a good club and they’re doing well so there’s going to be interest from outside.
“It’s up to us to try and convince them to stay.”