The England youth international has progressed through Everton's academy and is now attracting attention after making an impressive start to the current Premier League campaign.
Armstrong's route into senior football began with a loan move to Derby County ahead of the 2024-25 season, when he gained experience in the Championship. He subsequently spent a spell at Preston North End before returning to Merseyside and pushing his way into Everton's first-team plans.
The midfielder made six starts and seven substitute appearances in the Premier League during the second half of last season, but has taken a further step forward in recent months.
He has started all nine of Everton's league matches this season and provided one assist, establishing himself as an important option in the centre of the pitch.
Those performances have reportedly attracted Chelsea's attention as they consider ways to strengthen their midfield options.
According to journalist Simon Phillips, who has close connections to Chelsea, the London club are following Armstrong closely and have already been in contact with his representatives.
No formal offer has been reported, and it remains to be seen whether Chelsea decide to turn their interest into a concrete approach.
Armstrong was also the subject of attention from Nottingham Forest during the summer transfer window, although he remained at Everton.
The teenager is under contract at Goodison Park until the summer of 2028, giving the club a degree of protection against potential approaches.
Chelsea's reported interest reflects their continued attention to young talent capable of developing into a long-term first-team player. Armstrong's experience in the Premier League, despite his age, is likely to make him an attractive prospect.
For Everton, retaining a player who has quickly become a regular starter will be important, particularly with his development now attracting interest from another leading English club.
Any potential move remains at an early stage, with Chelsea continuing to monitor his progress rather than having made a formal bid.