Levein has moved for Pernis after seeing Lukasz Zaluska move to Celtic and Michael McGovern also depart the club.
Pernis, who is under contract with MSK Zilina until the end of December, has inked a pre-contract agreement with United.
United are hoping to secure an early release with MSK Zilina to allow Pernison to make the move to Tannadice ahead of the new SPL season.
If United fail to secure Pernis' early release they are expected to sign another goalkeeper on a short-term deal.
Zaluksa meanwhile has been unveiled by Celtic on Monday after a successful two-year spell at Tannadice.
The Poland international thanked Levein for taking a chance on him and predicted continuing good times at Tannadice.
He said: "I would like to thank Dundee United and the coach and all the supporters, because it's thanks to them I am sitting here today.
"They gave me the opportunity to become successful in Scotland.
"I think the Dundee United coach is that good, he loses good players every year but he still manages to be successful."
Levein had already signed goalkeeper Steve Banks from Hearts as a player/coach, but the 37-year-old is expected to provide cover for the first-choice keeper.
Coach Scott Thomson and former Celtic youngster Michael McGovern left the club after the end of the season.
Meanwhile, United also revealed that Ryan Dow is going on loan to Forfar Athletic, while midfielder Ross McCord will be loaned to Stirling Albion.