Betis narrowly avoided relegation from the Primera Liga last season after finishing in 16th place, and are currently busy rebuilding their squad.
Gonzalez, who previously spent a year on loan with Real Sociedad, is thought to be close to finalising his transfer, along with Portuguese goalkeeper Ricardo and Argentina striker Mariano Pavone, after failing to establish himself at Anfield.
"We will do everything possible to create a team that is strong but that also has a winning mentality," said Cuper, who was confirmed at Betis on Monday after signing a one-year contract.
"The important thing is that this team has a strong personality.
"They (the club's prospective new signings) are all very good players. Ricardo has a great mentality, Pavone has played well for two years in Argentina and Gonzalez can improve a lot."