The Huddersfield Town striker has already been linked to two of Crystal Palace's Premier League rivals.
Grant has scored nine goals in 15 Championship games for Huddersfield this season, attracting interest from two of Crystal Palace's Premier League rivals, Wolverhampton Wanderers and Bournemouth, according to The Sun.
The latter publication has speculated that the former Charlton Athletic player will cost in excess of £10 million if he changes clubs in January.
And The South London Press claims that a sell-on clause would see some of that - thought to be more than 10 per cent - heading back to Charlton, who recouped £2m at the start of the year.
Crystal Palace have been linked to a succession of strikers ahead of the winter window, namely Olivier Giroud, Alfredo Morelos and Michy Batshuayi.
Grant, who scored four goals from his first nine Premier League starts, would be another appealing proposition.
And being a south Londoner himself, the 22-year-old could be attracted by a move to Crystal Palace.
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