The 23-year-old was expected to sign a long-term deal last season but negotiations stalled in part over his wage demands.
Abraham ended up triggering an automatic one-year extension last July, tying him to the club until 2023 and earning him a small increase on his £50,000-a-week wage.
That extra 12 months reduced the urgency to find a longer agreement but sources have told ESPN that both parties are now likely to wait until the end of the season before reviewing the situation.
Abraham enjoyed a breakthrough season at Stamford Bridge last term after years spent out on loan, scoring 18 goals across all competitions and scoring his first England goal at senior level in a 7-0 win over Montenegro.
Chelsea moved to tie down Reece James, Fikayo Tomori, Mason Mount and Callum Hudson-Odoi to long-term deals and were expected to do the same with Abraham but it is understood they were reluctant to offer Abraham a six-figure weekly salary.
He has started just 12 Premier League games this season and is sidelined with an ankle problem that will rule him out of Gareth Southgate's England squad for this month's matches against San Marino, Albania and Poland. Abraham is also thought to be wary of speculation that Chelsea will look to sign another striker this summer.
Competition will be fierce with Manchester United, Manchester City and Paris Saint-Germain among a host of top clubs interested but the mere fact the Blues are in the running is viewed by some as ominous for Abraham's playing chances in the future.
He has started just four times under Thomas Tuchel with his only goal coming in February's FA Cup fifth round win at Barnsley.