The 20-year-old midfielder has attracted the attentions of the two Premier League clubs following some impressive performances for the Ligue 1 outfit this season.
It is believed that both have made contact with Bastia over a possible deal for the France Under-20 international.
It is thought Newcastle lodged a £3 million bid for Thauvin, which was quickly turned down by Bastia, while Arsene Wenger has enquired about the availability of the former Grenoble midfielder.
But reports coming out of France now claim that Bastia president, Pierre-Marie Geronimi, has told both interested clubs they must be ready to spend at least £6 million for the Ligue 2 club to even consider doing business.
Thauvin, who is contracted to Bastia until 2015, has made 20 appearances in all competitions for the Les Bleus so far this season, finding the net on three occasions.
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