The Chelsea youngster was once regarded as the brightest talent in the club's academy but his refusal to sign a new long-term deal has led to him being frozen out.
According to the Daily Record , Brendan Rodgers' side want to emulate their free transfer deal where they secured the highly-rated youngster, Moussa Dembele, from Fulham last summer.
Celtic could sign him without paying the full development fee that English clubs would have to, meanwhile Liverpool and West Ham have been linked with a move for Solanke in the past few months. The development fee for English clubs is thought to be around £8 million for Solanke, while Celtic could get him for as little as £400,000.
WHO IS DOMINIC SOLANKE?
Solanke is a forward who has played for England at every under-age level and he was once crowned the country's Youth Player of the Year.
England won the UEFA European U-17 Championship with Solanke as their top scorer in the competition in 2014.
He has won the FA Youth Cup and the Uefa Youth League with Chelsea's famed academy. He was also crowned Chelsea's Academy Player of the Year in 2014-15 after scoring 41 goals across a variety of age groups. In the same season he made his professional debut, coming on off the bench against Maribor in the Champions League.
Jose Mourinho made it his personal mission to see him and said: "My conscience tells me that if, for example, [Lewis] Baker, [Izzy] Brown, and [Dominic] Solanke are not national team players in a few years, I should blame myself."
Solanke ultimately ended up at Vitesse on loan in 2015-16 and he had an indifferent spell, scoring seven goals in 25 games, in his first full season as a professional footballer. In 2016-17, Solanke has made few appearances in Chelsea's youth teams but he has been an unused substitute in the first team on two occasions under Antonio Conte.
WHY DIDN'T SOLANKE BREAK THROUGH AT CHELSEA?
Solanke has found first-team chances limited this season with Chelsea unwilling to push a player who won't sign a new deal. Chelsea require their young players to renew contracts before they send them on loan but, with Solanke refusing to sign, he has found himself available for a transfer.
The situation led to a stand off between the player, who is represented by his step-father, and the club. Antonio Conte finally addressed the situation at a press conference two months ago.
"I don’t know [about his future] I should have a crystal ball to tell you about his future," the manager said. "For now he is at Chelsea, I don’t know about his future. Is he leaving? I don’t know, I think this is his will."
"It is best to ask him [why]. I think for a young player to stay in a great team like Chelsea is a great opportunity. You have to respect his decision."
Chelsea will be unhappy to lose Solanke, who was regarded by those around the club as just as good as Tammy Abraham, who produced a stunning breakthrough season at Bristol City this year.
WHO WANTS SOLANKE?
Celtic appear to be the strong favourites due to their unique placement to exploit his availability on the cheap, but Liverpool and West Ham have been linked with a more expensive move in the past.