Dyche on Sunday dropped Joe Hart and handed Tom Heaton his first Premier League start in 15 months following injury, and was rewarded with a clean sheet in a 2-0 win over West Ham.
Pope, who earned an England call-up for his performances filling in for Heaton last season, is nearing a return from his own shoulder injury and Dyche will consider him for the FA Cup clash against Barnsley at the weekend.
"Popey is getting closer," Dyche said. "He's training all the time now virtually, so he needs to get at least one more game into him. Possibly we'll consider it for the cup game, because he's that clear.
"He's been training with us for about a month, and we have to be careful, we have to give him the chance to be right.
"And, of course, there's the competitive element with the other goalkeepers. Tom has come in and delivered a very good performance."
The return of Pope – who was injured in Europa League action in the summer – would leave Dyche trying to balance the ambitions of three goalkeepers who are eager to remain in the thoughts of England manager Gareth Southgate.
Heaton, who made an outstanding late save to deny Andy Carroll on Sunday, is expected to start in goal again when Burnley return to Premier League action on Wednesday night away to fellow strugglers Huddersfield.
That match could also see Robbie Brady return to action following a hip injury, though it will come too soon for Steven Defour and Stephen Ward.
"Robbie's got a chance, Steven I don't think will," Dyche said. "Wardy is getting closer, but needs match time.
"Steven's not really serious, it's just making sure, to make sure he comes back.
"Robbie's has just been a knock, a very slight tear in his hip abductor, it just needing settling down, but he's been back on the grass training and he's clear at the moment, so he's got a chance of coming back into the thinking."