West Ham United are said to be keen on the winger, who could have been playing in England already.
However, the Rennes winger is said to have proposals from two of the Hammers' divisional rivals.
Grosicki was heavily linked with Everton during the summer transfer window, and the report claims he saw a transfer to Burnley fall through at the eleventh hour, despite flying in to finalise the move.
The collapse is said to have left Grosicki 'mad at the world', although the 28-year-old has made a swift return to form - scoring three goals and assisting one in his last eight outings.
West Ham are by no means short of wingers, however, Besiktas loanee Gokhan Tore has been tipped to return to his parent club early in January, which could free up a space for the right-sided player, who has 48 caps for Poland.
Grosicki is not the only wide man to be linked with Slaven Bilic's side this week, with the Irish Herald reporting that Hammers scouts have been deployed to watch Dundalk's Daryl Horgan in the Europa League on Thursday.