Abraham has 12 goals in all competitions this season, making him the Blues’ leading scorer, but he was left out of the squad to face Manchester United on Sunday by new manager Thomas Tuchel.
The Hammers are in desperate need of another striker after selling Sebastian Haller to Ajax in January, leaving them with Michael Antonio as their only senior option for the rest of the season.
Antonio has performed admirably since being converted into a striker by David Moyes, with seven goals in 17 appearances for West Ham, who sit fourth in the table, a point ahead of rivals Chelsea.
Abraham is unsure about his long-term future at Stamford Bridge as rumours continue that the club will make a move to sign Borussia Dortmund’s Erling Haaland this summer.
The 23-year-old has faced increased competition for his place in the Chelsea team this season following the arrival of Timo Werner.
Although Werner has struggled since his £47.5million move from RB Leipzig last summer, he has much more top-level experience than Abraham, and it’s hoped that Tuchel’s appointment will help him rediscover his best form.
Abraham came through the ranks at Chelsea, making his debut in May 2016, but then had spells on loan at Bristol City, Swansea City and Aston Villa before finally establishing himself in the first team last season.
His cause was aided by Chelsea’s transfer ban, which encouraged Frank Lampard to rely on several young prospects, including Fikayo Tomori, Reece James and Mason Mount.
But when the ban ended, the Blues spent heavily on new players and Abraham fears that the arrival of someone like Haaland will see him shunted even further down the pecking order.
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