Lindsay impressed at Ross County during the 2017-18 campaign.
The 22-year-old midfielder made 26 Scottish Premiership appearances for The Staggies during the campaign, but failed to help County stay in the top flight of Scottish football.
He has shown that he is more than capable of plying his trade at the top level north of the border, and may want to remain in the Scottish Premiership next season - or indeed look for a move down south.
But County are keen to re-sign the midfielder, who has little chance of breaking his way into Celtic's side at the moment. Lindsay is set for showdown talks over his Celtic future in the coming weeks, with the knowledge County want him.
The 12-time Scotland Under-19 international has just two weeks remaining on his contract, which could help County complete a permanent move for the exciting midfielder.
With the likes of Scott Brown, Kouassi Eboue, Olivier Ntcham, Stuart Armstrong, Callum McGregor, Ryan Christie and Scott Allan all in Brendan Rodgers' thoughts, Lindsay is likely to be told he can leave.