The Denmark international has been without a club since leaving Fiorentina last summer.
An Achilles injury prevented him from turning out during his final season with the Viola, meaning he is short on match sharpness, but he is looking forward to linking up with a side currently sweating on their top-flight status.
The 33-year-old, who took in a brief spell at Everton in 2005/06, is expected to pen an agreement with Pescara before the weekend.
Kroldrup's agent Ippolito Gallovic told tuttomercatoweb.com: "There are only a few details left to arrange.
"Both sides have shown a willingness to get things done. Now Pescara have to check everything and complete a physical test."
Pescara sports director Daniele Delli Carri added: "I can confirm that the player will sign an agreement until the end of the season, with an option for another year."