Signing a new attacker is top of the Chelsea wishlist currently, given the lack of cover behind Nicolas Jackson with Armando Broja and Christopher Nkunku both having suffered serious injuries in the past year.
Jackson has had a mixed start to life at Stamford Bridge too, after being dropped recently, but he did reclaim his place and scored a hat-trick away to Tottenham Hotspur and Chelsea's third in their 4-4 draw with Manchester City in recent weeks.
Football London claims that a deal for Osimhen is unlikely to happen during the season, given the fee they would likely need to pay to acquire the player.
The club paid a nine-figure fee to bring Enzo Fernandez to the club last January, but appear reluctant to fork out a similar sum this time around.
Ivan Toney is also on their shortlist of options, and will demand a lower fee, with the Brentford striker likely to leave the club after he returns from his current eight-month suspension for breaches of gambling rules.
However, the report states that Chelsea remain undecided about whether they will enter the market for a new striker in January, or wait until next summer.
That is partly due to the fact that Nkunku is set to return to first-team duty very soon, and the club have high hopes that he can hit the ground running in a blue shirt.
Nkunku scored 58 goals in his final two seasons with RB Leipzig and broke into the notoriously competitive French national side before his injury, but fitness issues have plagued him over the last 12 months.
Broja has also proved a useful option for Mauricio Pochettino after returning from a serious knee injury, and the Albanian won
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