The Germany international is reportedly attracting interest from Barcelona amid speculation of a clause in his contract which would allow him to leave the club next summer.
Talks between the 21-year-old and the Bundesliga club are ongoing, and Eberl believes he has been able to provide enough arguments to convince ter Stegen to choose the Foals over Barca.
"We've had some very good talks," Eberl told the Rheinische Post newspaper.
"In the end, it is up to Marc to decide.
"There are many advantages for him to stay here and Marc is a clever guy, but for sure we need an answer at some stage."
Ter Stegen is understood to be keen on Champions League football next season as he seeks to dislodge Manuel Neuer as Germany's number one.
With Borussia Dortmund's Roman Weidenfeller called up for Germany's next two friendly matches, ter Stegen can no longer be assured of his place in the national team squad for the World Cup next summer and the lack of European football is placing him at a disadvantage.
However, with a third of the season gone, the Foals are currently on course for a top-four finish, which would provide one of those "advantages" to convince ter Stegen to remain where he is.
"It's a very positive moment for us," said Eberl.
"We deserve this league position given the way we have played, but we still have a lot of work to do."
Eberl has a lot on his plate dealing with contract renewals for Juan Arango, Filip Daems, Roel Brouwers, Martin Stranzl and back-up goalkeeper Christofer Heimeroth, although his priority remains ter Stegen.
"We know their quality and I'll be the first to talk to them, but there is no rush," Eberl added.
"We will make the right decisions, but we have also got to hear what the players expect. Everything has got to be right."