manager is expecting to have both Dwight McNeil and available when Everton host on Saturday.
McNeil missed the goalless draw with West Ham last time out due to a knee problem, while Branthwaite did play in that match but pulled out of international duty with England due to a minor groin issue.
It seems likely that both will be involved at Goodison Park on Saturday at 3pm when the Toffees host the Bees, though.
Dyche confirmed that both have been in training, and while he could not guarantee they would play this weekend, the signs look good.
‘Dwight’s had a really good week training,’ Dyche told a press conference on Thursday. ‘Jarrad trained today after settling things down, so we’ll see how he responds.
‘We’re hopeful on that but he should be ok.’
Dyche’s side has lost just one of their last seven Premier League games, so they are proving difficult to beat but it has not been thrilling stuff.
The goalless draw with the Hammers came after a 1-0 loss at Southampton, with draws against Newcastle and Fulham earlier this month and the only win in November coming at Ipswich.
Everton have been hampered by injuries, though, with a number of players still out.
Starting with Armando Broja, Dyche addressed his other injury worries, saying: ‘He has had a full week’s training but he does need a games programme obviously.
‘We’re looking at the dates now as we wanted to ensure he came through his first full week. He said he feels good and feels fit so we’ll introduce a games programme once things align.
‘Youssef [Chermiti] is making good progress as well. He’s slightly behind (Broja) but had his first full day with us today, which was pleasing.
‘Seamus [Coleman] is on the grass with the medical side, just taking the first steps back. Jimmy [Garner] has had good news from the specialist but has been out a while and is going to have to be careful in the initial spell.
‘Tim [Iroegbunam]’s stress response in his foot is clearing up so he can start sort of semi loading again and making sure he starts his progress back.’