The Spaniard is an odds-on favourite with Sky Bet to be Everton's next manager as the Merseysiders face the prospect of losing David Moyes to Manchester United.
But Martinez, who takes Wigan to Wembley for Saturday's FA Cup final with their Premier League status under threat, has previously turned down approaches from Aston Villa and Liverpool.
Whelan said: "It's a battle that I will lose and Wigan will lose, I've no question on that.
"But would Roberto choose to go to Everton or would he wait for one of the really big clubs?
"I'm not degrading Everton in any way, shape or form - they're a great club with great supporters - but is Everton regarded as one of the top European clubs? Well, unfortunately they're not."
Whilst Martinez is the favourite, Swansea's Michael Laudrup, former Toffees striker Mark Hughes, Cardiff's Malky Mackay, Neil Lennon of Celtic and Porto's Vitor Pereira have all been mentioned as possible options.