Burnley boss Sean Dyche has offered no update on the possibility of him joining Everton, but didn’t rule himself out of the running.
The Toffees have yet to appoint Ronald Koeman’s successor, with caretaker David Unsworth preparing for a fifth game at the helm this weekend.
Allardyce and Dyche were two of the first names in the frame when the Dutchman was sacked last month.
But with other targets emerging – including Watford’s Marco Silva – the former England boss publicly withdrew from contention.
Dyche, who is preparing for Swansea’s trip to Turf Moor on Saturday, was keen not to speak about the Toffees but stopped short of putting the links to bed.
“It’s amazing you’re still asking. As I’ve said plenty of times before I’m just getting on with what I do here. Everyone must know that by now, surely,” he said.
“I’m at the stage I’ve always been at, I’ve had plenty of speculation, in a good way mostly, and that’s part and parcel of everything we’ve achieved here. You get interest, whether it’s me or my players. But I’m still here, simple as that.”
There is a sense that it would be better for the Clarets if the Toffees were to make their position known sooner rather than later, with Dyche’s future the dominant topic of discussion for several weeks now.
Midfielder Jack Cork, one of six England debutants during the international break, can understand why the manager might be in demand but hopes it blows over.
“I would like him to stay, he’s shown faith bringing me here and I’d like to repay that,” said the former Swansea player.
“There’s not many English managers with a CV like his in the game, especially with what he’s done at this club. He’s got two promotions to his name and keeping the team up last year was a great achievement.
“If something does happen it’s out of our control, we’ve got to keep doing what we’re doing.”
There has been confusion over Burnley top-scorer Chris Wood’s fitness during the international break, with the striker reduced to substitute appearances in each leg of New Zealand’s World Cup play-off defeat to Peru.
He would usually be first choice but the All Whites felt he was not able to manage 90 minutes due to an apparent hamstring issue.
That does not chime with Burnley’s assessment when they cleared him for the long trip, and Dyche said: “I think over that side of the world they weren’t sure he was ready to start for them, so we’ll catch up with him on Friday.
“Our medical team have obviously been in contact and I don’t believe there’s anything too major there, a bit of tightness, a bit of soreness maybe. We’ll get eyes on him and see if he’s fit.”