The young attacker has been in impressive form on loan at Lecce, and his good performances have supposedly earned him the interest of the Serie A giants
Luis Muriel has been one of the revelations of the season at Lecce and has already scored seven times in 23 Serie A appearances this term.
The youngster's good performances have not gone unnoticed elsewhere, and a summer move could be on the cards.
"My agent has made it known to me that AC Milan and Inter have made official offers for me," Luis Muriel said to RCN Mundo.
"The only thing I know is that I will return to Udinese at the end of the season. There are some offers though, so we'll see what happens."
The attacker joined Udinese from Deportivo Cali in the summer of 2010, but has yet to make his official debut for the Zebrette.