Having missed two matches with a hip flexor issue, the 36-year-old frontman returned in Wednesday’s 3-1 Premier League win away in West London.
“Cristiano is a question mark because he has a problem with his neck,” Rangnick told MUTV.
“He received treatment yesterday for two or three hours and we will have to wait to see how he feels today.
The United boss also suggested Edinson Cavani was a doubt for what could be a crucial game in the race for the top four.
“Edi (Cavani) hasn’t been training with the team yet and will hopefully resume training today and then we’ll take the final decision after the training session today, if he will be available for the game tomorrow.”