AC Milan have made an offer for Zlatan Ibrahimovic in an attempt to shake off competition from other interested clubs, according to Sky in Italy.
The club would like to bring the former Sweden international in to train with the team next month, so that he can be match fit from January.
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Developments are expected next week when Milan officials and Ibrahimovic's agent meet again.
However, Ibrahimovic's salary demands are currently too high for Milan to proceed with negotiations, as the Italian giants are serving a ban from European competition due to Financial Fair Play breaches.
Napoli and Bologna are other Serie A clubs showing an interest in the 38-year-old striker, but are yet to put forward any formal bids to his representatives.
Milan are currently 14th in Serie A and have scored 11 goals in 12 matches in the Italian top flight so far this term.
Ibrahimovic played for Milan between 2010 and 2012 and scored 56 goals in 85 games during his time the club, helping them to the Serie A title in 2011.
The forward's contract at LA Galaxy officially expires in December. He scored 31 goals in 31 games during the last MLS campaign.
When does the January transfer window open?
As the January transfer window inches ever closer, clubs across the Premier League, Europe and beyond will be identifying potential transfer targets and holding discussions with clubs and agents over future deals.
At this traditionally difficult time to make big moves, the start of the new year looks set to be frantic for a host of top Premier League clubs.
Where can you follow all the latest transfer news?
As well as keeping an eye on Sky Sports News, you can make sure you don't miss a thing with our dedicated Transfer Centre blog.
There will also be the return of the Transfer Talk Podcast and some exciting new features coming your way...