The Brazilian striker originally left the Sao Paolo club for Real Madrid in 2005, before returning to his homeland on loan towards the end of an unsettled two-year spell with Manchester City.
Now into his third season with Milan since moving to Italy for 18million euros in 2010, reports in Brazil have suggested the player and his former club are keen to unite for a third time.
But ahead of a Coppa Italia meeting with Reggina, Allegri told the Corriere dello Sport: "Robinho is a champion, an extraordinary player, just think about his goal against Torino - I'm talking more about the dummy before the shot than the actual shot!
"I know he has admirers all over the world but he will stay with us and will be an important player for the second half of our season."
Robinho scored 14 goals in all competitions as Milan won the Scudetto in the 2010-11 season, before adding nine as the Rossoneri finished as runners-up to Juventus last season.
A stunning strike against Torino last weekend marked only a second goal of the current campaign, though, and the 28-year-old has admitted he carries Santos close to his heart.
He told Globoesporte: "I have history with Santos.
"It won't be difficult for them to reach a deal with me. My love for that club is eternal, but there are also other clubs interested and who are talking to Milan.
"I am a professional and will see what is best for me. Milan do not want to sell me and I have no intention of arguing with a side that opened its doors and gave me a chance."
Santos president Luis Alvaro Riberio told atribuna.com yesterday: "Robinho wants to return to Brazil and for him that means returning to Santos.
"We have presented a written offer, though there is a difference between what the player and the club are asking for.
"It is not an easy negotiation process, but we will know the outcome next week."