The 24-year-old appears set to leave the Scottish Premiership leaders in the near future.
The Scottish Sun reports that the 24-year-old appears to be heading for the Parkhead exit in the near future after he rejected a new four-year contract last month. And with his current deal expiring in December, it seems unlikely that the summer window will pass without the Scotland international moving on.
And while Celtic may have still hoped that they may be able to tempt Forrest into staying - based on the fact that they were previously willing to put a long-term extension on the table - Palace's interest may make his mind up that he wants to leave.
Although he may have been cautious about the interest from the two clubs already in the chase for his signature - seeing as Rangers are some way off the Championship play-off places, while the Canaries could soon be joining them in the second tier as they currently find themselves in the Premier League relegation zone - Alan Pardew's side look to have enough daylight between themselves and the bottom three to suggest that they will be in the top flight next term, which may be what sways Forrest towards Selhurst Park.
However, the competition in the Eagles' squad may count against them in their hopes of signing their target. The likes of Wilfried Zaha and Yannick Bolasie can be devastating on the wings when they are on form, while Forrest has come in for criticism this term for his inconsistency, which may make it difficult for Pardew to justify dropping one of his other players to get the Celtic man in the side.