Cardiff have turned down one enquiry from an unamed club with Bluebirds boss Dave Jones saying: "We've had one enquiry for him and Jay knows about the enquiry."
Asked if the enquiry had come from a Premier League club, Jones said: "Well I would hope so. If it was someone in our division or below what is the point of him leaving Cardiff?"
Bothroyd is out of contract in the summer and is now free to talk to other clubs and Jones continued: I'm sure Jay won't mind me saying: Jay wants to stay at this football club.
"We are trying to get him to sign here and I spoke to Jay yesterday in training about trying to get some sort of deal done, and that is ongoing
"Even the club we spoke about, Jay says he doesn't want to go to.
"We said no [to the approach] and Jay knows about it, because his contract is up in June and people think they can come and take him for a measly amount of money. It's not worth what we are trying to do.
"So keep him and get the best out of him and then if he decides to stay with us or he decides to leave then that's what we will do. He wants to try and sort it out here, but he is entitled to try and get the best deal for him.
"If we want him to go because we have been offered vast amounts of money then Jay can say no because he is under contract."