The 25-year-old, whose Oakwell expires in the summer - with discussions regarding a new deal having yet to reach a successful conclusion - has been linked with a move to several Championship rivals including Millwall, Cardiff, Middlesbrough and QPR.
Confirming that the club have knocked back a bid for the former Leeds United player, he said: “It is a fight with (to keep) Alex, for sure. He has played a great season, so far.
“We have rejected an offer from another club. We have made a good offer to Alex to extend the contract.
“Now, for sure, Alex has to think about (it) and to discuss to try and find the best solution. It is a normal situation, actually. We give everything to keep him here.
“This guy is very good for the club. For the team, he is the captain and is more than the captain, he is a face and identification for the way to play football.
“It would be a very important sign to extend his contract and that is why I have told the club that we have to do everything to get him to extend his contract. We need this.
On the potential for Barnsley to lose Mowatt for free this summer, if he goes not sign a new deal by the end of the window, he added: “Sometimes, in some negotiations, money is not all. In this situation, Alex Mowatt is more than only ‘sell and buy’.
“We have to fight to keep him, for sure and he has a choice to make his decision and we have to accept it.
“But our purpose is to fight until the end, so Alex signs a new contract.”
Meanwhile, Ismael has confirmed that Liam Kitching and Jordan Williams faces spells out of action.
Recent signing Kitching is suffering from a groin problem, while Williams - who recently returned from injury - is sidelined with another separate issue.
Ismael, who says that Aapo Halme is due back in training, said: “We have some good news and bad news. The bad news is that we have two injured players with Liam Kitching and Jordan Williams again.
“Jordan came back and when he is ready for the next step, he gets another injury. We hope it will be a short one (absence), maybe two weeks.
“He (Liam) has an ongoing issue (groin injury). We have so many games and we cannot take any risks.”
No positive tests have been recorded among Barnsley’s players in the latest round of testing, with more tests to take place on Friday.