Now, with the August 31 deadline looming, it seems as though Hoops fans may have their worst fears realised as the Frenchman may be on his way out of Parkhead.
The 22-year-old, a £500,000 bargain capture from Fulham two years ago, has emerged as a top Marseille transfer target with the Ligue 1 club keen to bolster their strikeforce before the window shuts.
According to RMC, Marseille have contacted Celtic and, although the Scottish champions will do everything in their power to retain Dembélé’s services, the player is said to be ‘open’ to the prospect of making the switch to the Vélodrome.
Although time is running out, it’s safe to assume that Celtic – who will be approximately £18million richer – will at least make an effort to sign a replacement.
Here are five options they should consider.
The Dutchman is a different type of player to Dembélé, whose game is built more on speed and swift changes of direction.
However, Celtic have Odsonne Édouard as a like-for-like replacement for Dembélé and Janssen is a far better striker than his travails at Tottenham Hotspur would have you believe.
The 24-year-old struggled to make an impact in his first season at Spurs but any player who finds the net 31 times in a season (Janssen achieved that for AZ Alkmaar in the 2015/16 season) clearly has the makings of a decent frontman.
He is currently injured, however, and uncertainty over the extent of his absence may ward off potential suitors.
The talented Dane enjoyed a breakthrough campaign with Ajax in 2016/17 and while he couldn’t replicate his 23-goal haul last term, he remains one of the brightest prospects in the Dutch Eredivisie.
The 20-year-old was not a guaranteed starter for Denmark in the World Cup and will be keen to make a big impression this season.
He ruled out a move away from Ajax earlier this summer but that cannot be taken as gospel considering the highly capricious nature of the transfer market.
Seán Maguire (Preston North End)
Maguire was scouted by Celtic before he joined Preston last summer.
The former Cork City frontman has seen his stock rise dramatically at Deepdale over the last 12 months.
He scored nine goals in 18 games during an injury-hit first campaign in the Championship, form which was enough to see him break into Martin O’Neill’s Republic of Ireland squad.
The former West Ham United forward has not played yet this season due to a hamstring injury but, when fully fit, he would be a strong option for fellow Irishman Brendan Rodgers.
A natural finisher with sharp movement in and around the box, Maguire has his best years ahead of him and could be a shrewd addition for the Scottish Premiership holders.
The Iranian star has long been linked with a move to Glasgow. Last year, the Hoops were one of a clutch of clubs – including Fulham and Everton – reportedly interested in the 23-year-old.
Dubiously dubbed ‘the Iranian Messi,’ has impressed in the Russian Premier League with Rostov and Rubin Kazan.
Azmoun also played every minute of Iran’s World Cup campaign in Russia but sensationally announced his retirement following his country’s elimination from Group B, which included Spain, Portugal and Morocco.
Making the switch from Russia to Scotland would be a considerable culture shock but for a player of Azmoun’s natural gifts, it’s certainly an environment in which he can thrive over time.
Injuries have ravaged the talented England striker’s career but the 28-year-old appears to have regained his fitness.
Eager to get minutes under his belt, Sturridge joined West Bromwich Albion in January last season but failed to score in six appearances for the Baggies.
And, while he scored immediately after coming on in Liverpool’s 4-0 win over West Ham on the opening day of the season, the fact that he has only played a combined 11 minutes in the two games since suggests breaking into Jürgen Klopp’s first team will be a difficult task.
Scott Sinclair revived his career north of the border and there is no reason why Sturridge couldn’t do the same. When fit and with a run of games under his belt, the former Chelsea forward offers pace, excellent movement and finishing.
And let’s not forget; Sturridge played the best football of his career under Rodgers during Liverpool’s run to second place in the 2013/14 season. It would be an intriguing narrative if his former manager were to offer him a lifeline.