According to the Daily Mail's Jack Gaughan, the Chile international's agent is trying "to gauge the level of interest" in the forward by "sounding out" various clubs across Europe after a disappointing start to Sanchez's career at United.
Sanchez, 29, joined United in January in a swap deal with Henrikh Mkhitaryan.
The move was widely seen as a major coup for the Red Devils, as Manchester City had also been heavily linked with the forward.
However, the former Barcelona man has been surprisingly poor since moving to Manchester.
He has netted only three Premier League goals in 18 appearances and does not seem to have benefitted from a free summer after Chile failed to qualify for the 2018 FIFA World Cup.
His late winner in United's most recent outing against Newcastle United ended a lengthy scoring drought, per Squawka:
Per Gaughan, Sanchez's recent split from his long-term girlfriend Mayte Rodriguez has been cited by some sources as a reason for his poor form.
But he has been lacking his usual cutting edge since he joined United and may struggle to attract interest from other clubs, even if he does want a move.
Per BBC Sport, Sanchez signed a four-and-a-half-year deal worth £14 million per year after tax when he joined United.
Few clubs would be prepared to match those wages, especially given his form.
It is therefore unlikely Sanchez will be going anywhere anytime soon, and United fans will be hoping he can rediscover his best form as they look to recover from a poor start to the season.