Reports over the weekend suggested that the capital club may be keen, but Andrea D'Amico knows nothing of their alleged interest.
"There has been no contact up until now between Gattuso and Lazio," he told Radio Mana Mana Sport.
"Once his Milan stint ends then we will meet up to decide his future.
"Gattuso is considering a number of situations, countless, but not Rangers seeing as they are only allowed to sign players under the age of 18.
"I've had a variety of offers and he still wants to play football, but there has been no approach from Lazio.
"The player now needs to just find the right solution."