Tillman spent last term on loan at Rangers from Bayern Munich and the Gers had an option to keep him on a permanent basis, which they did not take up.
Sheffield United have been looking to sign him from Bayern Munich and have been in competition with PSV Eindhoven.
Now Tillman looks set for the Netherlands, with PSV Eindhoven in the final stages of talks with Bayern Munich, according to Sky Deutschland.
Tillman will join the Dutch club on a season-long loan.
PSV Eindhoven will pay a loan fee of €1m for Tillman, while they will also have an option to buy set at between €12m and €14m.
The club finished second in the Eredivisie last term and have Champions League football on the agenda.
Tillman could potentially come up against former club Rangers in the Champions League in PSV Eindhoven colours this season.
