
The crucial pair have not been spotted in the club's training footage at all this week, ahead of the trip to London Stadium amid their fitness scares.
Downes came off early with an ankle ligament injury against Norwich City last Wednesday, and he missed the 0-0 draw with Bolton Wanderers altogether.
Larin, meanwhile, has a minor hamstring issue and was forced off before half-time against Bolton last time out, after back concerns earlier this month.
Eckert has refused to rule them out of the meeting with promotion rivals West Ham, but he has a history of giving overly optimistic updates on players.
Ahead of the match, he said: "Flynn is getting better day after day, will assess him today and he's doing everything to be involved tomorrow.
(Image: Stuart Martin)
"Cyle's issue is part of the hamstring towards the tendon, the bottom part, but it's the same for him. He's trying everything to make it for tomorrow.
"It's different, his back is fine, this just came from the collision."
There was guaranteed good news on the status of Caspar Jander, who was left an unused substitute last time out against Steven Schumacher's side.
The German midfielder played over 70 minutes midweek at Norwich, due to Downes coming off, when medical advice suggested he should not play.
Jander is returning from a quad injury suffered in the first game of pre-season at Eastleigh, and made his first appearance in the south coast derby.
"Last week has been a little bit more than he was supposed to play, but then you see the way he performs, and it looked like he's ready," said Eckert.
"We took him on the bench against Bolton, but that was more for an emergency, so the clear plan is that he gets a break on that Saturday.
"He's had a very good week, so he'll be involved tomorrow."