The 16-year-old centre-half took in two spells at Anfield during January and February, allowing him to catch the eye of the Reds' coaching staff.
With Liverpool eager to bring the best European talent into their youth set-up, an offer is set to be made to Polgar.
His representatives are confident that an agreement will be reached to take the promising youngster to England on a permanent basis.
Tibor Pataky, director of the Careers Management Group which owns Polgar's registration, said: "Kristof trialled with Liverpool on two occasions earlier in the year, and he and his parents are currently in Liverpool enjoying the hospitality of the club.
"We are looking forward to an exciting day, and in a few days the Hungarian presence at Liverpool will be extended."
Liverpool already have Hungarian goalkeeper Peter Gulacsi in their first-team squad, while Krisztian Adorjan is captain of their U21 side.
This is what we need to do if we want to compete with the likes of Man City and Chelsea: Concentrate on trying to bring in top quality young players from around the world. Of course there will be some hit n' miss but it could save us a lot of money, which we could then use on 2-3 top quality signings per year. An example would be Rafael at the scum. He's becoming a pretty decent player and could be their right-back for the next 8 years.- raklfc