The midfielder has made Gareth Southgate's squad for the Three Lions' games against Germany and Lithuania this month
England travel to Germany for a friendly on March 22 before hosting Lithuania in a World Cup qualifier four days later
Livermore moved from Hull for £10million in January and has made six appearances for the Baggies ahead of Saturday's Premier League visit of Arsenal.
His only cap came in a friendly against Italy in 2012 and Pulis urged the 27-year-old to impress as Livermore aims to become the first outfield Baggies player to feature for England since Steve Hunt in 1984
He said: "I still think we'll see the best of him next season
With Jake it was just important to get him to a club where he felt a lot more secure
coming here he feels at home
That's the best way of describing it
"He's got the opportunity and that's the great thing
He has the opportunity to train and show what he can do
"He's a wonderful kid
He's come into the club and if you speak to any of the players they'll tell you what a great character he is
He's pretty old school, works hard and get his job done but also has a great sense of humour."
Football Association technical director Dan Ashworth previously held a similar role at the Baggies and called Pulis to discuss Livermore at the start of the week
Pulis said: "I spoke to Dan, he'd rung me earlier in week, so I knew there was something, but didn't know he was selected
He asked me about the kid, my thoughts.
"It is brilliant for Jake, now I hope he really pushes on, gets a real identity about his game to put him in position where he knows his strengths and weaknesses
He's got all the tools to be a really good player."
The Baggies host Arsenal after back-to-back defeats to Crystal Palace and Everton and will be without Matt Phillips (hamstring) and James Morrison (ankle)
Pulis added: "As I said when we were doing well, as sure as eggs are eggs, we'll hit a spell where we lose games
The important thing is to dust yourselves down and move on to the next one
It's a real test for everybody, all the players who are available, to get the points that we want."
Source : PA
Source: PA