The 21-year-old has missed Liverpool's last seven games in all competitions due to the metatarsal fracture that he sustained in the September international break, although he was recently pictured back on the grass at the AXA Training Centre.
Elliott's return to outdoor running fuelled optimism that he could be available for the weekend's visit of Chelsea, or failing that Liverpool's Champions League showdown with RB Leipzig in Germany on October 23.
However, speaking to Sports Mole, Lynch admitted that the former Fulham starlet is not expected to be back for either of those games, saying: "The initial hope was that he'd be ready straight after this international break, but I think the Chelsea game is currently looking pretty unlikely, and maybe even the game after that.
"He might need just a little bit more time, but he is getting closer and to get him back to play a role in these games that are coming up... it's going to be pretty relentless with midweek-weekend again all the way through this season."
Would Liverpool still be unbeaten had Elliott stayed injury free?
Prior to picking up his foot injury, Elliott had only played seven minutes in Liverpool's first three games of the campaign, coming off the bench in the 2-0 win over Brentford either side of being an unused substitute against Ipswich Town and Manchester United.
The England Under-21 international's absence has exposed Liverpool's lack of depth in the middle of the park, as Alexis Mac Allister and Ryan Gravenberch have started all nine of the Reds' games across the Premier League and Champions League so far this season, while Dominik Szoboszlai has featured from the first whistle in eight of them.
Curtis Jones is the only other Liverpool midfielder to start a Premier League game this season, as neither Wataru Endo nor Tyler Morton have got into Arne Slot's good books yet, and Lynch has suggested that the Reds should try to bolster their engine room in the January transfer window.
However, Lynch also insisted that Elliott will have a "massive role" to play in an unforgiving period of fixtures for Liverpool, and he also questioned whether the 21-year-old could have made a difference in the 1-0 loss to Nottingham Forest, the Reds' only loss of the season so far.
"He would have played so much football already this season and so [Mac Allister] would have got a little bit more of a rest at some points, because that's a really nice change that you've got there that you can make between games," Lynch added.
"But he's getting closer now and I think these coming games he's going to play a massive role, and Liverpool are going to need him. They haven't quite missed him so far this season because they've been doing really well, but he's a really high quality option to bring in.
"Maybe even think of that Nottingham Forest game against a low block - he would have been a really helpful substitute in that one. But he's back now and the hope is he can play a big role in the games to come."
Elliott has come up with 10 goals and 15 assists in 120 appearances for Liverpool since arriving from Fulham in 2019, and it remains to be seen if the midfielder will be able to make his comeback against Arsenal on October 27.
Will any other Liverpool players return against Chelsea?
Elliott is one of three injury concerns for the Liverpool medical team to deal with at present, as Alisson Becker is out for the long-term with the thigh injury he suffered in the 1-0 win over Crystal Palace on October 5.
Summer signing Federico Chiesa - who has experienced a disrupted start to life at Anfield - also missed that clash with an unspecified concern, and his availability for the visit of Chelsea also remains clouded in uncertainty.
The Reds hold a one-point lead at the top of the Premier League table after seven gameweeks, but they could be overtaken by Arsenal should the Gunners win their game against Bournemouth on Saturday evening.