A deal has been agreed for the 21-year-old right-back, who has been playing for Ferhervar in his homeland.
And as long as the final details are all sorted out as expected, he will be signed before swiftly heading out to Switzerland.
Bolla was part of Hungary's 26-man Euros squad. He did not play in the tournament but made the bench against Germany, having previously won two caps.
He made 12 appearances as Ferhervar finished third in the Hungarian top flight last season and is set to link up with Grasshoppers after their promotion to the Swiss Super League.
The Zurich club are owned by Jenny Wang, the wife of Fosun chairman Guo Guangchang, with Wolves also having Leo Bonatini and Tote Gomes on loan there.
Meanwhile, Wolves have added a sixth friendly to their summer schedule.
As part of their upcoming warm-weather training camp in Marbella, Bruno Lage's side will go up against Las Palmas.
The first friendly of the summer is at League One Crewe this Saturday, after which they will travel to Spain.
Already in place for the trip was a friendly with Real Betis on Saturday, July 24, and now they will also face Las Palmas on Monday, July 26.
The game will take place at 9.30am BST and be streamed live on Wolves TV.
Wolves – once back in England – also have friendlies against Stoke, Coventry and Celta Vigo before the 2021/22 Premier League campaign starts.