The north London club are searching for a new manager as Arsene Wenger’s 22-year spell at the helm draws to a close.
Allegri, who can win the Italian double if they beat AC Milan in the final of the Coppa Italia tonight, is one of the possible candidates lined up to replace Wenger.
However, he would not comment on the speculation linking him with a move to the Premier League.
“At the end of the season, we’ll sit down and talk as we always do and plan for the future,” Allegri said in quotes published by Football Italia.
My growth process isn’t finished yet and I hope it’ll only end when I have decided to retire, which won’t be too late. I do have a few more years in me.
For his part, Wenger said he has no part to play in selecting his successor.
But, speaking ahead of tonight’s trip to Leicester, he did offer a word of advice, suggesting the incoming boss retain some of the backroom staff currently in place who have a feel for the history of the club.
Of course people who come in also want their own staff, that’s about finding the right adjustment. Personally, I always tried to have a local person, who knows the culture, who knows the habits, the tradition and makes sure you don’t make the mistakes.
Wenger has hinted he may be tempted by a job away from day-to-day club management after leaving Arsenal.
The 68-year-old will step down following Sunday’s clash at Huddersfield, ending a spell of almost 22 years in charge of the Gunners.
Since news on Wenger’s departure was made public last month, the Frenchman has refused to be drawn on what he intends to do after leaving Arsenal.
A break from the game looks likely but, despite suggesting management is where his heart lies, Wenger would not rule out the possibility of a different role — whether that be higher up within the structure of a club or working as a general manager.
Asked if it was his desire to remain as a day-to-day manager, Wenger replied: “That is what I have to decide.
“I have not made the decision so at the moment I would say yes, spontaneously yes. But maybe with a distance I will think, ‘No, maybe it’s a time to change a little bit of direction.’ Honestly, I can’t give you an answer. I don’t know.
But I enjoy going out there every day, of course. You know I didn’t miss a training session in 22 years, I never stayed in my office. Every day I was out there. That is something that I will miss.
Wenger has been linked with a role at Paris St Germain but insists his relationship with the club’s chairman Nasser al-Khelaifi stretches only to media commitments with his beIN Sport television network.
Meanwhile, Leicester boss Claude Puel has no plans to give his former manager a gift as Wenger leaves the Gunners post.
But he does want to welcome the 68-year-old to the King Power Stadium in a friendlier way than when the pair were on the training ground at Monaco.
“One time the ball was between him and me and I touched the ball. But behind the ball there is Arsene and he flew up in the air,” said Puel.
“He fell on his back and he couldn’t move. The fitness coach took him in the dressing room and I had a bad feeling.
“The other players were smiling and I was thinking in this moment ‘it is finished for me and I will not play in the future’.
“It is not a lack of respect but the intensity of the training you need to have. Quickly I played the next game, it was OK. Of course he will get a friendlier welcome.”