Starfelt did not start for Celtic in their Scottish Premiership opener against Ross County on Saturday and Bhoys boss Brendan Rodgers admitted after the game that he could leave the club.
Celtic went with new boy Maik Nawrocki with Cameron Carter-Vickers as their centre-back partnership in the 4-2 win.
Sutton though believes that Celtic should not be rushing Starfelt out of the Celtic Park exit door, as the Bhoys will need strength in depth at the back.
“I don’t think Celtic should be in a rush to get Starfelt out the door”, Sutton wrote on Twitter.
“CCV and Nawrocki maybe first choice but if anything happens to them.”
There remains a month left in the summer transfer window and Celtic could look to bring in a replacement for Starfelt if they let him go.
Next up for Celtic is a trip to Pittodrie to lock horns with Aberdeen, before a Scottish League Cup tie against Kilmarnock.
