The 22-year-old Dutch midfielder has been heavily linked with a move away from Heerenveen this summer following a solid season at the club.
Rangers have long held an interest in the midfielder, but it seemed for a while that they would be focusing on other options.
Heerenveen have already rejected a €5m offer from Hellas Verona and it has been claimed that Rangers are now moving the needle to sign him.
According to Dutch daily De Telegraaf, the Scottish champions have touched base with the agents of the midfielder over a potential summer move.
Gerrard is an admirer of the midfielder and wants to take him to Ibrox during the ongoing transfer window.
The Rangers manager believes that he can help the 22-year-old midfielder to further develop as a player.
Heerenveen have been holding out for a fee of around €10m for Veerman, but Rangers are claimed to be only ready to offer around half of it at the moment.
It remains to be seen whether Veerman pushes for a move to Rangers in order to work under the tutelage of Gerrard.
