However, his absence from Southampton's pre-season training camp has led to the speculation that he could return to the side that made him a club and international star.
Supporters were understandably excited at the prospect and made their feelings known on Twitter.
@celticcommunit1 wrote: "Stuart Armstrong didn’t travel to Austria for their pre-season training camp. No formal links have been made yet, but, make it happen, @CelticFC."
@CrumbsTMT said: "I'd launch any midfielder not named Callum McGregor out of Celtic Park with a trebuchet if it meant Stuart Armstrong coming back."
@P__67 added: "Stuart Armstrong back? F*****g YES! He’ll also come back a far better player after a year in the Prem, which he done well in. Also we get to sing his song again obvz."
While @Kitson67 tweeted: "Stuart Armstrong returning would be a dream. Get him in that 10 role ASAP. Also can he play right back?"
Although, not everyone was positive about the rumour.
@melbourne88 said: "I’ve no idea if Stuart Armstrong is any good or not and neither do you, drap the act."
But mainly fans were a bit skeptical at the idea of a player who performed reasonably well in the English Premier League last season would come back to Scottish football - and at an affordable price.
@FrankBtin insisted: "Stuart Armstrong is not coming to Celtic. Anyone who believes otherwise needs to get a grip on reality."
@seanmarkus_67 [email protected] "Stuart Armstrong coming back would be the highlight of 2019, will never happen but."