The two centre-backs potentially face life on the bench at Old Trafford as Eric Bailly and new signing Victor Lindelof look set to be the starting centre-back partnership for the Red Devils.
The two England internationals have two years remaining on their current deals and Pulis has previous success at luring Man United players away from Manchester.
Pulis has signed Darren Fletcher and Jonny Evans during his time in charge of the Baggies and will be hoping that Jones and Smalling are the next additions.
27-year-old Smalling was once considered United’s best centre back but since the arrival of Eric Bailly and also the great form of Marcos Rojo before his horrific injury last season, the Englishman has been pushed down the pecking order.
The same goes for Jones, 25, who has not really been tied down to one position during his career but Pulis sees this as a positive.
Pulis is a huge admirer of both players and loves the fact that Jones is versatile and can play more than one position which is exactly what the manager is looking for.
Both players don’t want to be spending time on the bench and want to be regular starters to ensure that they are in the England squad for the upcoming 2018 World Cup in Russia.