The Latics supremo revealed that Martinez was never happy with the offer from Anfield and believes that Villa "are not big enough" to be able to tempt the Spaniard from Lancashire.
"Roberto is staying at Wigan and, of course, I am absolutely delighted. He was never offered the job at Liverpool because he wasn't happy with the way the job was presented to him," Whelan told Sky Sports.
"He has had some talks with Villa, but he's not going to go there. Villa are a fantastic club with great fans, but I never thought they were big enough for him.
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"I've said all along that I never thought he would end up there, and, fortunately for us, that's how it has turned out.
"If Roberto is to go anywhere, it will be to one of the top clubs in Europe. We're just so pleased that he's staying with us for another season."
Whelan also revealed that he will be looking to extend Martinez's contract at the DW Stadium after guiding the Latics to Premier League survival last season.
"We've discussed a lot of things and it was a productive afternoon. He's got two years left on his current contract and we will be looking to extend that.
"We've also agreed to build up the academy and the training facilities.
"We want Roberto to be happy at Wigan and we'll be aiming to make sure we do everything to help him."