"We've turned down an offer for Jonny", Pulis said on Friday.
City are planning to return with another offer for Evans, rumoured to be in the region of £22m, in order to test Albion's resolve.
'We've turned down an offer for Jonny, ' Pulis said. "Jonny is one of our best players and we'd love him to stay".
But Pulis, who says he wants to keep Evans at The Hawthorns, added: "It would need to be a very good offer".
"He is happy here, he has just been made captain and wants to get on with his football".
Evans came through the youth ranks at Manchester United and won three Premier League titles and two League Cups at Old Trafford before being sold to West Brom by Louis van Gaal in 2015.
"Every player is for sale at the right price", admitted Pulis. "And then we would sit down and talk to Jonny about the situation". But Pulis says West Brom are under no pressure to cash in on their new club captain.
West Brom centre-back Gareth McAuley and midfielder James Morrison are also ruled out of the trip to Burnley as they are recovering from thigh and knee injuries, respectively. "Until all parties agree nothing will happen". So we're not desperate to get the money.
"I think what it shows and proves is that the transfer market should close before the season starts", Pulis said.
Tottenham are advanced talks to sell defender Kevin Wimmer to West Brom for £15million rising to a potential £20million, according to a report.
"Whoever's telling you we're close is miles away from the fact", he said. "We've got a lot of irons in the fire and we hope to get deals done and they have to be right for the football club". And he'll be good in the dressing room for the younger players.