The 27-year-old striker has been turning heads this season with his goalscoring feats in the Bundesliga and is not expected to stay in Germany for too much longer.
He has 16 goals in eleven league appearances this season and several clubs in the Premier League are interested in snaring him away from Stuttgart.
Newcastle, who are tipped to do business next month amid their injury crisis, are firm admirers of Guirassy and could make a move.
Manchester United and West Ham also have their eyes on him, but according to German outlet Fussball Transfers, the chance of staying at Stuttgart has not been ruled out yet.
It has been claimed that a move to the Premier League appeals to the forward ahead of the winter window.
However, Guirassy could still agree to stay at Stuttgart until at least the end of the season, with a move in January by no means guaranteed.
The German club could do little if he is keen to leave and a club trigger his €17.5m release clause and the Premier League may well appeal to Guirassy.