His contract expires next summer and could leave on a free transfer, but Jones played down suggestions Bothroyd had turned down an offer.
"I really don't know, you don't know with Jay, he just wants to concentrate on his football," said Jones.
"That's fine, it isn't a problem.
"At the moment, I'm comfortable with it, he's comfortable and we'll just keep chipping away and see what we can do."
Former England under-21 international Bothroyd is the Championship's top-scorer but his all-round link-up play is crucial to Cardiff's Premier League promotion push and makes him one of the most influential strikers outside the top-flight.
Bothroyd joined Cardiff from Wolverhampton Wanderers in August 2008 on a three-year deal and has flourished hitting 33 goals in 87 league games.
The Arsenal academy graduate, who scored in his only England U21 cap against Mexico, has settled at his eighth club after a nomadic start to his career which took him to Italian side Perugia.
And Jones believes he can keep hold of the Londoner.
"He knows what we're all about here and he knows what we're trying to do, and I'm sure he wants to be part of that," added Jones.
"We might have to wait until the end of the season and he sees where we are.
"I'm the only manager ever to offer him an extension."