The former Arsenal midfielder's contract expires in the summer and he know he will not be short of offers to play elsewhere.
That has been the case since last summer when Coppell decided he would continue to pick him even though contract extension offers had been spurned.
But now Sidwell is set to be left out of a Premiership fixture for the first time despite having recovered from a foot injury in time for Saturday's home clash with Fulham.
Coppell explained: "He will be fit enough to play but given the hullabaloo that is going on at the moment and given the fact we have five games I may just leave him out to see how we do without him.
"I want to see quite a few different permutations between now and the end of the season. I want to make changes to see how people react.
"I don't want it to be an experiment and I'm not going to make massive sea changes every game. I just want to see who can play with who and who can physically cope.
"I have spoken to Siddy and told him I might leave him out for a couple of games to see how we do without him and he fully understands."
Coppell still harbours hopes the 24-year-old might stay but knows this will only be the case if rivals see him as a squad player.
He said: "I have not given up hope of him staying but realistically the odds are very heavily against him staying. That is not a reflection on us but on his ability and the desire of other clubs to try to use him.
"I would still say that he has to think very carefully about the decision he makes because I don't think he would be comfortable in rotation. He is a player who thrives on the physical demands of playing every week."
Saturday's game will be the first for new Fulham manager Lawrie Sanchez, who has replaced the sacked Chris Coleman until the end of the season.
Sanchez, who is also continuing as the Northern Ireland manager, began his playing career at Reading and still lives near the town.
Coppell said: "He comes to watch us quite a lot so I would suggest he has seen us more than most Premiership managers.
"I don't know him well but what he has done in management and what he is doing with the Northern Ireland team you can only compliment him and he will be wanting to make an immediate impact."
PA Sport