The 22-year-old, who has been capped twice by Denmark, was the second-highest scorer in the Danish league last season with 16 goals from 33 league games.
Aalborg's new sports director Allan Gaarde has revealed the two clubs have yet to reach a compromise on the fee following an initial round of talks, although they are closing in.
"We had a long debate, but we've not quite agreed," said Gaarde, speaking to Nordjskye.
"However, we are close, so we have given Nicklas permission to travel to Birmingham at the weekend and look at the situation."
Addressing the talks between the two clubs, Helenius said: "I hope AaB will show enough co-operation and not demand too much money for me.
"The market is not ready for big transfers at the moment.
"I have already secured the club a lot of money through my goals, and I am on my first professional contract, so I am not making an awful lot of money."
Given manager Paul Lambert's policy of letting young players make a name for themselves, Helenius is naturally eager to join the club.
"Aston Villa is a very exciting club known to use young players," added Helenius.
"I therefore think the club will be taking me to England and letting me play. I do not want to come to England to sit on the bench."
If a deal can be ironed out, Helenius would become Lambert's second acquisition this summer following the recent capture of Aleksander Tonev from Lech Poznan.
Lambert is also understood to be closing in on a move for another Denmark international in 20-year-old Ivorian-born centre-back Jores Okore who currently plays for Nordsjaelland.