Since he arrived at the Liberty Stadium from Rayo Vallecano for £2m last summer, the Spanish attacker has scored 21 goals in all competitions, including one during yesterday's League Cup final victory over Bradford City.
Despite the reports, the 26-year-old has insisted that he is "living a dream" with the Swans.
"I don't know but I hope to stay here. I'm very happy at this club. Swansea has brought me my first title and I'm living a dream here. I always say the same [thing]," he told Sky Sports News.
According to Spanish journalist Guillem Balague, Swansea would not consider parting with Michu for anything less than £30m.