Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
The Japan international was unveiled on Wednesday as a new Rossonero player having moved to the San Siro outfit on a free transfer from CSKA Moscow.
"I am really enthusiastic and excited," Honda said to AC Milan.com. "I'm truly happy.
"I have always followed Milan since I was a boy and I wanted to become a champion here. I know all of the Rossoneri players of the past.
"In Japan, the Serie A is a tournament that is followed a lot.
"I have chosen the number 10 jersey because I always dreamed of playing in Serie A wearing that number. Now I need to prove my worth on the pitch."
Honda revealed that former AC Milan manager and current Japan coach Alberto Zaccheroni welcomed his move to the Serie A.
"Zaccheroni encouraged me to come here," he said. "He told me that Milan are a great club and that I would like the city."
The 27-year-old attacking midfielder could make his Serie A debut in Sunday's game at Sassuolo.
"I don't know if I will play this weekend because I haven't played for a while," Honda said. "I know the fans expect a lot from me.
"I know I will have to score a lot of goals and provide plenty of assists. I need to play and win.
"I would like to win the scudetto, perhaps next season."
Milan are 11th in the standings, 27 points behind Serie A leaders Juventus heading towards the halfway point of the season.