The former Chelsea forward has endured mixed success at Barcelona this season, making only sporadic appearances and operating largely as a reserve to Samuel Eto'o.
United are apparently keen to recruit a new striker this summer with Louis Saha's ongoing injury troubles and Alan Smith's future undecided.
The English champions have been strongly linked with the Iceland international but his father, Arnor, insists Barca will not make a decision on his future until after this weekend's La Liga climax.
He said: "Honestly, I have not heard anything from Manchester United. I can confirm that.
"It's only speculation. I think the club will decide many things after the weekend and what is going to happen after the game (against Gimnastic).
"Then, maybe you might see a clearer picture of what's going to happen. But at this stage, nothing."
Asked whether his son would be willing to stay in Barcelona, Gudjohnsen said: "Probably. He's very happy there.
"He hasn't played so much after Christmas, but he came in before Christmas when Eto'o was injured and did quite well.
"So he actually wants to have another chance next season to prove himself even more."
The forward has been ruled out of Barca's final game in Tarragona, when they must better Real Madrid's result to have any hope of retaining the title they have won in the last two years.
Barca announced on Friday that tests revealed Gudjohnsen has inflamed cartilage in his right knee, keeping him out for around a week.