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Player of the year Rodriguez signed a new deal in March, which will run to the summer of 2013.
But QPR boss Neil Warnock is a fan of the Burnley-born striker, once describing him as a “super player”, and after having a £2.5million offer for 24-goal Championship top scorer Danny Graham rejected by Watford, he could step up his search for fresh firepower.
Howe said he hadn’t heard anything from the Championship title winners, but admitted they would be wasting their time if they did get in touch about the 21-year-old.
“We’re not open to any offers for Jay, and we won’t encourage any either,” said the Clarets boss.
“He’s had a fantastic season and he’s a big part of our plans.
“I’ve not heard anything from QPR, but if I did, they would be told to go away in no certain terms.”