The 28-year-old is in the peak of his career and has netted 27 goals in 25 matches this term.
Per Sport Bild in Germany, United are looking at Guirassy as a rotation option for Rasmus Hojlund.
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The Denmark forward has impressed in his first season at United, but is the only fit recognized striker.
Guirassy would not come cheap, given Stuttgart would want to hold onto their chief goal threat.
However, he may be seen as a slightly more affordable option, compared to the likes of Victor Osimhen and Ivan Toney.