Medel cost £9million from Sevilla last summer, but it is not expected that he will remain in south Wales ahead of next season following Cardiff's relegation from the Premier League.
The Chilean is widely reported to have a relegation release clause, and Solskjaer admits that Medel, who will be playing in the World Cup finals, will not be featuring in the Championship.
"Gary is a top, top player who deserves to be playing at a higher level than the Championship and he has proven that," admitted Solskjaer.
"Nothing has come up yet, no offers have been received for Gary."
Solskjaer also confirmed he had received enquiries for a number of his players, with reports suggesting that England international defender Steven Caulker and Scottish goalkeeper David Marshall could also leave.
"We have a big squad and it's not sustainable to have that amount of first-team players on contract," said the Norwegian.
"I have spoken to players, had chats to them.
"The wheeling and dealing has already started."