The new Portuguese coach confirmed the signing of French midfielder Youssouf Fofana from Monaco is nearly complete, with no other recruitment planned.
He would join striker Alvaro Morata, and defenders Emerson Royal and Strahinja Pavlovic, who signed for Milan earlier in the window.
"After his [Fofana's] arrival, our incomings will be completed, we will need to focus on outgoings," Fonseca told reporters on Friday.
"Some players must leave now. We have many, and it's not easy to work with a lot of players.
"We work and play to aim for the top, we cannot say that we are ahead of everyone to win the league, but we want to be fighting for the Scudetto.
"Inter are reigning champions, we know their level. Juventus, Napoli and Atalanta, apart from ourselves, also have the right things to compete."
Fonseca has only been Milan's coach for two months but has overseen an unbeaten pre-season in that time, and he is pleased with how his players have adapted to his methods.
"I came to Milan at the right moment in my career," he added. "The feeling is very positive, right from the first day, we have already improved more than I expected.
"We are expecting a different and more complex game than those we have played in pre-season. We want to show our identity from the very first game."
Zaniolo has flourished in the Italian capital since arriving from rivals Inter in 2018 but he tore his anterior cruciate ligament (ACL) in January.
However, the 21-year-old returned to action on Sunday – coming off the bench in the 66th minute of Roma's 2-1 Serie A loss to Napoli in a huge boost for Fonseca's side.
"He had no more than 30 minutes, slowly he will become important again," Fonseca said post-match.
"He entered a difficult moment but tried to help the team. Soon Zaniolo will be ready to help the team."
Fonseca added: "It has been a positive moment, it has been a long time out and he is not yet in the best conditions to play many minutes.
"However, it was important for him to come back against a great team. Let's see how he responds during the week, we must be careful of this moment. Let's not forget that he's been out for a long time."
Roma lost their third consecutive game to be sixth in the Serie A table with eight matches remaining.
A lack of silverware is believed to be behind Kane's alleged urge to move on, with Manchester City, Manchester United and Chelsea the leading suitors.
In the post-COVID world where club finances have been hit hard, some clubs are getting creative.
TOP STORY - CHELSEA'S PLAYER-PLUS-CASH SWAP DEAL
Chelseaare launching a player-plus-cash swap deal to land Kanefrom Tottenhaminvolving goalkeeper Kepa Arrizabalaga and forward Tammy Abraham, claims ESPN.
Spurs keeper Hugo Lloris is expected to leave the club, hence the lure of Kepa who has been back-up to Edouard Mendy, while Abraham, who is not a regular starter for the Blues, could help to fill the void left by Kane.
Kane is contracted with Tottenham for another three seasons and Spurs are believed to want a transfer fee of £150 million, so the addition of players would drop that figure down to an affordable level.
ROUND-UP
- The Guardian reports that Sergio Aguero has agreed to a two-year deal with Barcelona, with his departure from Manchester City this off-season already confirmed.
- Arsenal's Sead Kolasinac will leave the Gunners, with Schalke 04 and Laziocircling for the Bosnian's signature, reports Football London.
- Fernandinhowas set to exit Manchester City, but The Times claims he will renew with the club on a one-year deal.
- The manager merry-go-round is in full swing, with The Mirror claiming that Wolves are looking at ex-Roma boss Paulo Fonseca, while The Sun reports that Tottenhamwill try to convince Brendan Rodgers to join the club if Leicester City fail to qualify for next season's Champions League.
