Slot is familiar with the Dutchman's qualities from his time in the Eredivisie, where Veerman has made a name for himself since joining PSV from Heerenveen in January 2022.
The 25-year-old commanded a fee of just €6m (£5.1m) to sign for the Eindhoven giants, whom he has now made 115 appearances for, scoring 22 goals and setting up another 40.
Veerman excelled in a playmaking sense last season, scoring seven goals of his own in 41 matches in addition to a staggering 19 assists, 16 of which came in the Eredivisie.
No player in the Dutch top flight set up more goals than Veerman in the 2023-24 season - Luuk de Jong was the closest behind with 15 - as he won an Eredivisie and Dutch Super Cup double.
Slot 'identifies' Veerman as ideal number six
The 25-year-old's form unsurprisingly led to a Euro 2024 call-up, and he appeared in all six of the Netherlands' games en route to the semi-finals, although he made headlines for the wrong reasons while out in Germany.
During his nation's 3-2 loss to Austria in their final group match, Veerman lasted just 35 minutes before being taken off in a tactical change, and he cut an inconsolable figure on the Dutch bench afterwards.
Nevertheless, the PSV man's exploits in the Eredivisie could still earn him a marquee transfer, as the Anfield Watch reports that Liverpool have shortlisted him as a potential midfield addition.
The Reds underwent a major midfield rejig last summer, but new head coach Slot is still thought to be keen to bring in a new number six who can also play a key role in building up attacks.
Veerman apparently fits the bill, and the 25-year-old is now in the final two seasons of his PSV contract, so the Dutch champions may not be averse to letting him leave for the right price in the coming weeks.
Alexis Mac Allister and Wataru Endo shared the defensive midfield responsibility last season, although the former is more effective further up the field, and the latter is already being linked with an exit.
Tyler Morton and Stefan Bajcetic are alternative options in the number six role, but RB Leipzig are pursing the former, while Bajcetic endured an injury-disrupted 2023-24 campaign.
Liverpool's Veerman interest could lead to part-exchange deal
As PSV are within their rights to ask for around £25m to £30m for Veerman, Liverpool's interest in the Dutchman raises the possibility of a part-exchange deal involving defender Sepp van den Berg.
PSV are thought to be leading the race to sign the centre-back as Liverpool hold out for €20m (£16.9m), a valuation that the Eredivisie side are yet to meet, but they could very well get their man as well as a small fee by letting Veerman head the other way.
Van den Berg previously slammed the Reds for hindering his future in an apparent clear indication that he wanted to leave, although he has since performed a U-turn on his previous transfer stance.