The 27-year-old scored in a rare start in the 2-1 win over LASK on Wednesday, but he was pulled off by Ole Gunnar Solskjaer after 60 minutes.
"Recently, he's not been good enough," said Scholes after the game. "To bring him off after an hour when he definitely won't start on Monday that was a little sign, and Fred as well, that he [Ole Gunnar Solskjaer] might be getting rid of them.
"I know what he's capable of, but at United he's just become a squad player. Unless there are a lot of injuries I don't see Jesse getting a run of games.
"I like Jesse, but I can't seeing him getting a run of games."