Abraham was the subject of a £25m deadline day bid from Spurs. The striker spent last season on loan at Swansea, netting five Premier League goals.
He bagged 23 in the Championship the season before at Bristol City and his record in front of the sticks impressed senior figures at Spurs.
Abraham also caught the eye of England boss Gareth Southgate, who handed the London-born player his first cap last year.
Tottenham have Harry Kane as their undisputed No.1 striker with Spaniard Fernando Llorente his main backup.
Son Heung-Min is also on the books but plays mainly in a wide position in support of Kane.
Even though Spurs’ reportedly lodged the mega offer, Chelsea had no interest in going through with the deal.
That’s despite Abraham said to have been keen on the switch from west London to north.
The striker could yet be on the move this summer despite the Premier League transfer window being closed.
Abraham is a target for Championship side Aston Villa, who can sign players on loan right up until next Friday.
Steve Bruce wants another striker on board to help fire his side into promotion contention in the second tier.
New Chelsea manager Maurizio Sarri has Alvaro Morata and Olivier Giroud on the books as senior strikers at the club.
Abraham is third-in-line for a game following Michy Batshuayi’s loan switch to Valencia for the season.
And Sarri may want to keep the England international around in case of injury and suspensions leaving him short.
When asked about his Chelsea future earlier this year, Abraham cited Spurs and Three Lions star Kane as a role model.
“He [Kane] is a player I have always looked up to and he is one of the greatest strikers,” he said.
”It gives me confidence that there is a light at the end of every tunnel, so it encourages me to keep pushing and try my best.”