Before this season, the Guinea international was not on the radar of some of the biggest clubs in Europe due to his modest form in France and Germany.
However, a career-best run of 17 goals from 14 Bundesliga fixtures and an alleged £17.5m release clause has led to the 27-year-old becoming one of the most sought-after frontmen in Europe.
With Stuttgart sitting in third position in Germany's top flight and holding a four-point advantage in the race for the Champions League, a transfer is far from a foregone conclusion.
Nevertheless, reports have consistently indicated that teams from across the continent are prepared to take a risk on the player before the end of the month.
In recent days, West Ham are said to have moved closer to the front of the queue for Guirassy as they contemplate how to bolster their forward line.
With Michael Antonio carrying a knee injury, Danny Ings not regarded as a regular starter and Divin Mubama having only just made the transition from the academy ranks, Jarrod Bowen has been used in an unfamiliar central role.
As a result of Guirassy currently being at the Africa Cup of Nations, though, the player does not necessarily have to be in any rush to decide on the next phase of his career.
According to Football Insider, Man United are monitoring the situation ahead of potentially trying to edge out their Premier League rivals.
At a time when Anthony Martial is expected to leave United in January or the summer, head coach Erik ten Hag will eventually require further competition in the final third.
That said, United have their FFP position to consider, a situation
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