'Players looking a bit brighter,' says Burnley boss Sean Dyche
Leading scorer Chris Wood could make it in time after training with the squad this week while fellow striker Jay Rodriguez is expected to feature.
Midfielder Dale Stephens is the other player more likely to travel after joining the depleted group on the grass at the Barnfield Training Centre.
Republic of Ireland international Robbie Brady, Dutchman Erik Pieters, striker Ashley Barnes and Icelandic winger Johann Berg Gudmundsson are not expected to play any part.
"It's still not amazing," said Dyche. "Woody has been out for a few days now training, which is good, Jay Rod had a couple of knocks that we've been keeping an eye on, but he seems fine.
"Johann isn't ready yet, I'll be surprised if he comes through it by Sunday, Robbie Brady is a 'maybe', Barnesy won't be ready for Sunday, Erik [Pieters] is 'touch and go' so we'll have to wait on that one.
"Dale Stephens trained today [Thursday] so we're hopeful on that one. It's a mixed bag really so two or three could figure and the rest we're still waiting."
The Clarets have had a rare window of opportunity to rest, recover and recuperate ahead of another trip to the capital.
Burnley have played 13 times in 42 games, which left the players looking 'jaded' in the goalless stalemate against 10-man West Brom at Turf Moor.
Dyche suggested his players had been 'well off it', adding that the congested schedule had caught up with them.
But he believes they are starting to look brighter after some respite. He said: "It's weird in the sense that we haven't had a break. It's useful really in terms of recuperation.
"I said in the last game we were way off the mark and looked jaded, tired after 13 games in 42 days and it caught up with us.
"We've got another three coming up. With the injuries we're asking a lot of the players that are being rolled out there constantly."
Dyche added: "That's the challenge of the situation; there are a lot of games and we have a lot of injuries.
"I wouldn't say it was 'likely', but it was 'possible'. Players are constantly playing with a lot of demand on them, we've got all the stats and figures for the output of the group.
"We gave them a couple of days off and they've been really good in training during the week and they look a bit brighter, so I'm pleased with that."