The Clarets have up to five games in hand on teams, after having one game called off for heavy snow, three after the opposition were unable to field a side, and the last two games, which Burnley applied to have postponed due to Covid and injury.
Burnley trained with only 10 senior players on Monday, leading to the re-arranged match at home to Watford, being called off, but the situation has improved over the week, with the side set for what would be a first league game in three weeks.
Dyche said: "They're beginning to come back, we're looking a bit healthier with Covid and injuries.
"Barnesy is still getting over his injury but beginning to get on the grass with us now, and it's good to see him around the group. He's not ready yet, obviously.
"Charlie Taylor is touch and go, he's got a knock on his foot in training last weekend.
"Erik Pieters is back in the building after the Covid thing, Johann and Erik trained with the group today, Dwight is back with the group, and Dale Stephens was back with the group for the first time today.
"Connor Roberts is okay...I think that's more or less everyone who was missing.
"It's been quite a long list...
"Woody going as well, Maxwel still away at least until next Wednesday.
"So a few coming back, but still a few missing."
Asked whether he would hope to be able to play at Arsenal, Dyche added: "I would hope so, yeah, we've had 16 out there today, so that's getting back to where the group wants to be.
"We should be fine."