Monk, 34, took charge for the "foreseeable future" following the sacking of Michael Laudrup last week and enjoyed a dream debut in the dug-out in Saturday's 3-0 derby win over Cardiff.
However, the likes of Everton assistant Graeme Jones, Ajax assistant Dennis Bergkamp and Feyenoord manager Ronald Koeman are all being linked with taking over in the long term at the Liberty Stadium.
Press Association Sport understands Monk will be in charge at least until the end of the season and is the board's preferred candidate for beyond the summer.
But the 34-year-old is not worried about speculation over the next Swansea manager.
"It doesn't bother me," he said.
"You could be in this job for 20 years and people would still be getting linked.
"That's part of football. It happens with players, with managers and even with owners.
"You just get on with the job and for me that means focusing on Stoke City. The only way I can work right now is by focusing on the next game."
Swansea have lost on their previous two visits to the Britannia Stadium in the Premier League, but a win there on Wednesday would give a substantial boost to their hope of remaining in the top-flight.
And Monk has made it clear there is no time to bask in the afterglow of Swansea's derby triumph.
"It was a great result against a local rival, but we have to build on it," he said.
"Our focus switched to Stoke as quickly as possible and that started on Sunday and we have had a good session today.
"I have told the players that mentally they have to switch on and they were focused in training and ready to build on the weekend.
"We are under no illusions as to how hard it will be but as long we give our best that's all we can ask."
Midfielder Jonjo Shelvey looks set to miss out again with a hamstring injury, but Michu has an outside chance of making his first appearance since mid-December after recovering from ankle surgery.
"Michu has been training, but has had a couple of days off as his ankle has swollen up a bit," said Monk.
"He did not train today, but he could be fit enough to play some part tomorrow so we have to wait and see.
"We all know what sort of a player he is for us after what he did last season, he is a massive player for us and any player like that adds so much quality to the squad can give everyone a boost.
"I've had good chats with him and we will build around him and it gives the team and the fans a lift."