It seems that Pulis is now looking to add some speed to his side, with reports suggesting that Swindon star Byrne is on his summer wish list.
The 22-year-old has played most of the season at right wing back under Mark Cooper, but last weekend's 4-0 defeat to Preston North End in the League One play-off final means Swindon could struggle to keep the pacey wide man at the County Ground.
Let go by Tottenham in 2013, Byrne has become a key player for Cooper and Swindon, leading to alleged interest from West Brom, who could look to pay up to £2m to land Byrne this summer, according to The Mirror.
Pulis may need a new right back having seen Andre Wisdom head back to Liverpool at the end of his season-long loan deal at The Hawthorns, whilst Cristian Gamboa has struggled to make an impact despite impressing for Costa Rica at last summer's World Cup.
Byrne is likely to be seen as the long-term solution at right back should West Brom pursue a deal for him this summer, with a move to the Premier League certainly too good to turn down for the League One star.