The 19-year-old winger joined the Hoops on an 18-month loan deal, as announced on the club’s official website at the time.
The England Under-19 international moved to City from London club Fulham in the summer of 2015.
Former Celtic striker Hartson has suggested on Twitter that Roberts is worth £15m.
The former Arsenal man made the suggestion during the pre-season friendly match between Barcelona and Celtic at Aviva Stadium in Dublin on Saturday evening.
Roberts started the International Champions Cup game and played for 45 minutes, and gave a good account of himself.
@JohnHartson10 u reckon theres any chance we could sign long term big man?— marc carrie (@arbroathcsc) July 30, 2016
Celtic will take on FC Astana at Celtic Park in the second leg of the Champions League qualifying third-round tie on Wednesday evening.