Speaking in his news conference on Wednesday, Besiktas coach Senol Gunes appeared to mock the England international for failing to turn up to training after he was allowed time off.
"Dele Alli could not come at this time," Gunes said. "It's raining, I guess that's why he couldn't come.
"We're trying to hear from him. We could not reach you by phone. Hopefully he didn't have an accident."
Alli responded on his official Instagram account following his manager's comments and said: "Hey guys just had loads of messages so wanted to clear something up.
"The club gave me permission to attend a doctor's appointment today. I'm due back in training tomorrow [Thursday] as normal."
Alli joined Besiktas from Everton on a season-long loan last summer but has struggled for consistency during his time in Turkey.
The 26-year-old has made 17 appearances this season and only scored three goals. He has been criticised by Gunes and was also booed off by his own fans when he was substituted during a cup match in December.
Alli has failed to maintain the heights he reached in the early stages of his career with Tottenham where he won back-to-back PFA Young Player of the Year awards during 2016-17.