The two London clubs are expected to be in the market for a new centre-forward in January, with Napoli's Osimhen and Brentford's Toney the names most strongly linked with a move to the Emirates Stadium or Stamford Bridge.
But both players now look set to stay with their current clubs beyond the upcoming transfer window.
Osimhen appears poised to pen a new deal at Napoli, with club president Aurelio De Laurentiis saying: "With Osimhen, we are about to sign the contract that was pending this summer."
Transfermarkt currently values the 24-year-old Nigerian international – who has scored 37 goals in 51 games since the start of last season – at €120m (£103m), but the Serie A giants are bound to demand more for their star man, especially if he does extend his stay in Naples, which may effectively price would-be buyers out of a transfer.
As for Toney, 27, the England international will be clear to play again from 17 January – having been banned from football since May after admitting to 232 breaches of FA betting regulations.
And Brentford boss Thomas Frank doesn't seem to think his 20-goal striker from last term – who has a £100m price tag – is going anywhere. He told The Standard: "I don't want to lose him. I hope, and think, he'll be a Brentford player on 1 February [the January transfer window closes at 11pm that day]".
While Arsenal are sitting pretty atop the Premier League table and Chelsea have shown signs of improvement under Mauricio Pochettino in recent weeks, neither club have had a player find the net 20 times in a league campaign since 2019/20.
Then, Pierre-Emerick Aubameyang notched 22 goals for Arsenal for the second successive season – having shared the Golden Boot with Liverpool duo Mo Salah and Sadio Mane in 2018/19.
No Chelsea player has reached the 20-goal mark since Diego Costa back in 2016/17.
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