Though Pulis believes the former Manchester United defender would have been fine at a bigger club, thanks to his experiences at Old Trafford, he is happy to keep him aboard and hopes to he will sign a new deal.
Evans was on a number of clubs' shopping lists during the summer, with Arsenal, Manchester City and Leicester City all failing in bids for the Northern Ireland worldwide, and now according to the Daily Mail, West Brom will look to make him the highest paid player at the Hawthorns with a new deal believed to be worth around £80k per week.
"We've brought a few players in".
Both men are lacking in match fitness so it remains to be seen whether they will be involved from the start at the Amex, or if they need to settle for places on the substitutes' bench.
"Gregorz is a little bit more rugged but technically very good as well".
"We will have to see if throwing them straight into a Premier League game is the right thing to do or not".
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A similarly tight encounter should be expected this time around as the pair attempt to get back on winning ways in the league. Wanyama suffered a knee injury in training prior to Spurs' draw with Burnley last month.
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'He's got to knuckle down to get back into the team and start showing everyone how good of a player he is again, ' said Pulis.
The defender has been nursing a hamstring injury but played in both of Northern Ireland's World Cup qualifying matches this month.
Arsenal are in action Saturday against Bournemouth while Evans and West Brom face Brighton on the same day.
Pulis insists Evans hasn't been affected by the speculation. If they'd have met the valuation it might have been a different situation.
"He's a very down to earth lad. He's very level-headed", said the Baggies boss. And I don't think the speculation fazed him'.