After a successful six-month loan with Betis, Antony and the LaLiga club are keen to extend the relationship.
Betis and United are in talks over terms and Fajardo told Marca: "Antony's is a very complex operation, we all need to be aware of it: because of the player's level, because of his recent experience at Betis.
"It's not easy, but until he has committed to another team, we will humbly play our cards to try to keep him. We will try different solutions without mortgaging the club, because sustainability is the most important thing.
"We will try to be creative, as we have done other times, to ensure that Antony stays. But with the economic rigour that we have always had. The market is open, very dynamic, and we are part of this game."
No surprise Antony wants to stay
Antony has already made it known that he wants to stay and Fajardo also said: "It doesn't surprise me.
"When a player arrives here and has such an immediate impact, it's not a coincidence: it's the result of work, sacrifice and the seriousness of everyone on a daily basis. So that Antony performs at his best and all the players who arrive here do the same.
"More and more great players are knocking on Betis' door, more and more big clubs want to collaborate with us, and more and more players who have left dream of wearing the Betis shirt again."