The 29-year-old has been a free agent since being released by Championship side Bournemouth at the end of last season.
And he says Rooney asked him to join him at Pride Park in the summer.
Wilshere said: "I did speak to Wazza actually, in the summer. It was when Derby were under that embargo where they couldn't buy anyone.
"And I went to Como as well, instead. And I thought about it, but it weren't for me."
Asked if he'd sign for Derby, Wilshere said on talkSPORT: "I don't know, it depends what comes up in January."
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