The 25 year old missed fixtures against Bristol City, West Brom and Hull City after picking up an injury against Huddersfield Town.
Saints went on to suffer defeats versus Bristol City and Hull having been unbeaten in 25 matches beforehand.
West Ham loanee Downes could return to the team for the visit of Millwall but Martin is yet to make that call.
Martin said: “Flynn has trained for a couple of days, we just have to assess how he has reacted from today.
“We’ll have a meeting with the medical staff like we do every week. Then we’ll make a decision.
“Whether he starts, whether he’s on the bench, whether we wait until Liverpool to give him more time.
“If he’s ready to start, brilliant, if he’s ready for the bench, brilliant, if he’s not we’ll give him more time.”
Millwall visit with their third manager of the season after Neil Harris was appointed this week to replace the sacked Joe Edwards.
The Lions sit 21st in the Championship table, hovering just one point above the drop zone after losing six of their last seven games.
Harris has already overseen a victory over Saints this season – when his Gillingham side dumped Martin’s out of the EFL Cup in the first round.
Martin continued: “It sums football up, and just how crazy it is that Neil is now in his third club this season.
Neil Harris is back in charge at The Den (Image: PA)
“Our team has been so different since then and I’m pretty sure lots of people watching that game probably thought we wouldn’t be in this job still by now.
“I’m really pleased for Neil. He’s back at the club that he is idolised and adored at. He understands the club, he’s managed them, he’s played there.
“I’m sure that’s a big reason why they’ve brought him back. It’s to get people to buy into him and to understand what Millwall are about.”
He added: “I feel for Joe (Edwards). It’s his first managerial job, it’s so difficult and I’m really sorry he hasn’t had the time to do what he wants to do.
“I just don’t like seeing anybody lose their job. Being in this position, I understand how difficult it is and how lonely it can be at times.
“We have a team with a new manager, someone who I’m sure a lot of the players will know, and they’ll have the fans right behind them.
