Speaking on the latest edition of Football Insider’s Inside Track podcast, senior correspondent Pete O’Rourke revealed that Armstrong, 32, has emerged as an option for the Scottish title winners and is very much on their radar.
However, sources say Brendan Rodgers will be looking for serious backing in the transfer market as he wants his team to make an impact in Europe.
As a result, the club will initially look at alternatives to Armstrong, with younger players on their radar who can develop and grow their games at Parkhead.
Finance expert Kieran Maguire told Football Insider that Celtic’s budget will have been given “rocket boosters” by their Champions League qualification.
Celtic consider transfer deal for Stuart Armstrong from Southampton
Armstrong has become available on a free transfer after leaving Southampton, opening up the opportunity for a return to Celtic after six years away.
The midfielder joined the English side for £7million in 2018, going on to make 214 appearances for the club in the Premier League and the Championship.
He made 45 appearances in the recently completed season, scoring six and assisting seven as he helped fire the Saints back into the Premier League.
Armstrong’s time at Parkhead saw him feature in both the Champions League and Europa League, while winning four SPFL titles, two Scottish Cups and two Scottish League Cups.
That winning experience, his European experience, and having previously established a strong rapport with the fans, have led to the possibility of a return this summer.
Armstrong is one of two former players Celtic are considering returns for this summer, with sources telling Football Insider that Kieran Tierney would love to return to Parkhead.
In other news, Caoimhin Kelleher is keen to quit Liverpool this summer.