The Swansea boss is reportedly one of the leading contenders to succeed Moyes, who is to leave Goodison Park at the end of the season to take on the huge task of filling Sir Alex Ferguson's shoes at Manchester United.
Wigan's Roberto Martinez, Cardiff's Malkay Mackay and Celtic's Neil Lennon are also thought to be targets for Everton chairman Bill Kenwright.
Laudrup was linked with the likes of Real Madrid, Chelsea and Manchester City earlier this season, before signing a new contract to extend his Liberty Stadium deal until 2015.
And the Dane re-iterated he will take the Welsh club into European competition next season.
He said: "It is pure speculation, like when some of my players are linked to other clubs or when players are linked with coming here, so I don't want to comment on it.
"I haven't spoken to anyone (at Everton), I don't have time I have so much work to do here.
"I don't have dreams of going to other clubs, I live in the present. I don't have dreams about what I am going to do in two, four or eight years because I don't know, I live in the present.
"I've said so many times my intention is to be here so I can't say any more than that."
Ferguson's decision to retire from management after a remarkable trophy-laden 27-year stint in charge at United means Swansea have the honour of being the Scot's last opponents at Old Trafford, and Laudrup does not believe Ferguson's marathon tenure with United will ever be repeated.
"You always know that one day we all have to stop, but it seemed Sir Alex would go on and on," he said.
"There were rumours a few years ago but this came out of the blue and caught us all by surprise, but it was going to happen and leaving after winning the title once more is the best way to go.
"What is unique with him is the time he has been at Manchester United. 27 years - even 10 years in other countries would be impossible.
"Here there is Moyes, Wenger and Fergie (who have spent over 10 years at their clubs) and that can only happen in the UK.
"In southern Europe there is talk of change after three years. To have five years at the same club is huge, so imagine 27 years at the same club.
"What makes it special is that it is his last home game so I'm very pleased and proud to be his opponent."
There have been those who have criticised the appointment of Moyes, pointing to his lack of a trophy during his 11 years on Merseyside.
And Laudrup acknowledges the former Preston boss faces a huge task.
"He's showed a lot at Everton, but it's a different level now and who can be prepared to fill shoes like that?
"It is one thing to win trophies, but I think it is the most difficult job in world football and Sir Alex is the most difficult man to replace."It was difficult for Tito Vilanova to replace Pep (Guardiola) after winning so many trophies in four years at Barcelona, but here he is replacing an institution.
"At least he has a lot of experience of the Premier League and the culture and I wish him the best of luck."