The Hammers have been one of the most active Premier League clubs during the summer window, strengthening their options in several areas of the pitch.
Niclas Fullkrug is a new addition to the final third, the Germany international having the credentials to earn regular starts in Julen Lopetegui's new-look side.
Nevertheless, according to Football Insider, West Ham have not given up hope of trying to tempt Abraham into a return to London.
Abraham missed the majority of the 2023-24 campaign due to a serious knee injury, but the 26-year-old is fit again and was used as a late substitute against Cagliari over the weekend.
Although it has been previously suggested that the England international intends to remain at Stadio Olimpico, just two years remain on his contract.
Fulham to sell Vinicius?
Meanwhile, Fulham may be prepared to cash in on a striker of their own in the form of Carlos Vinicius.
In his two years contracted to the Cottagers, the Brazilian has made just the 13 Premier League starts, a further 28 outings coming from the substitutes' bench.
The 29-year-old was subsequently loaned out to Galatasaray for the second half of 2023-24, featuring in the first XI on just one occasion with 11 appearances being made as a replacement.
Having not played during pre-season, there is an acceptance that his future is away from West London, and Sky Sports News reporter Dharmesh Sheth suggests that Las Palmas are the frontrunners.
A bid is said to have been made for Vinicius with Las Palmas seemingly returning to English football having already purchased former Sheffield United forward Oli McBurnie on a free transfer.
Sheth adds that Corinthians are also keen on Vinicius, who has not represented a club in his homeland since the 2017-18 campaign.
Palace identify Guehi replacement
Staying on the London theme and Crystal Palace have seemingly identified their ideal replacement for Marc Guehi, should they require one.
Newcastle United have failed with multiple offers for the England international with Palace rejecting offers in the region of £65m for the centre-back.
As it stands, it is unclear whether a resolution will be found that suits all parties, yet the Eagles need to have an alternative lined up in the event that they give the green light to a sale.
According to Sky Sport Deutschland reporter Florian Plettenberg, personal terms have already been agreed with Wolfsburg defender Maxence Lacroix.
While the two clubs have not settled on a fee, the expectation is that Palace would ultimately sign the 24-year-old if they receive their desired sum for Guehi.
The former France Under-20 international has spent the last four seasons with the Bundesliga outfit, scoring seven goals from his 129 appearances.