Sven-Goran Eriksson has made an enquiry about signing the 33-year-old striker on loan during the American Major League Soccer close season.
Henry has completed his first season with the New York Red Bulls, but is in England training with his former club Arsenal to maintain his fitness until the MLS season kicks-off again in March.
Henry has a 'multi-year' contract with the American club, and any deal will depend on whether the Red Bulls allow him out on loan, as fellow MLS club LA Galaxy did with David Beckham during the last close season.
Eriksson has already made two enquiries about Beckham's availability, but was told he would not be allowed to go out on loan again, while he also failed in a bid to sign Henry's former Arsenal team-mate Robert Pires, who joined Aston Villa instead.
Eriksson still believes Henry, who is Arsenal's record all-time goalscorer with 174 goals in 254 appearances during his eight-year spell at Highbury and the Emirates, has plenty to offer his side and his experience would bolster their promotion aspirations.
City have demonstrated their ambition to recruit big-name players and pulled off a coup by signing Nigerian international Yakubu on loan last week.
Meanwhile, Eriksson may take the opportunity tonight, in the FA Cup third-round replay at Manchester City, to follow up his interest in midfielder Michael Johnson, who is available for loan after returning from injury in a reserve game last week.
The 22-year-old is wanted on loan by several clubs, including Leeds United who he supports and has admitted he would like to join, but Eriksson has strong links with City.
Eriksson also has Mancini's teenage son Andrea training with City at Belvoir Drive. The striker is considered a decent prospect.
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