The 27-year-old is out of contract at the end of this season and Arsenal are not keen on losing him for free.
Crystal Palace are struggling to score goals this season and they could definitely use a striker. However, Welbeck is unlikely to solve their problems.
The Arsenal forward is a hardly the clinical option Hodgson is looking for. He could be a handy option for the Eagles but to rely on him for goals would be a mistake.
Palace need to sign a proven goalscorer if they want to save their season. It will be interesting to see what happens in January.
As for Welbeck, he is unlikely to start for Arsenal unless there are injuries. Leaving the club in January might be the best option for him.
He needs to play regularly at this stage of his career and that is simply not possible at Arsenal right now.