Swansea, Newcastle and Brighton have already made moves to sign the teenager who scored 26 goals during a successful loan stint in the SkyBet Championship with Bristol City last season.
But Celtic have asked to be kept abreast of any developments.
Tammy Abraham is wanted by a host of top clubsPA:Press AssociationTammy Abraham should has options for a move next seasonRex FeaturesTammy Abraham scored 26 goals while on loan at Bristol City this seasonRex Features
Abraham is currently in Poland for the Euro Under-21 Championship and will discuss the best option for his development with Chelsea when the tournament ends.
Brendan Rodgers and Hoops recruitment chief Lee Congerton know the forward from their time at Stamford Bridge.
Brendan Rodgers wants to add to his Celtic squadReutersTammy Abraham has been a huge success on loan at Bristol CityRex FeaturesTammy Abraham went close with a volley for England U21s vs SwedenRex Features
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Abraham has been part of the Blues’ academy since he was seven, spending four years under the watchful eye of Rodgers.
He is poised to sign a bumper £45,000-a-week contract with Chelsea when he returns from international duty.
Chelsea would prefer he joined another top-flight English club on loan, although Celtic qualifying for the Champions League group stage would help.
Striker Tammy Abraham is only 19 years old and has bundles of talent
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