Burnley are waiting to see whether a third offer will persuade West Brom to part with centre back Craig Dawson.
Burnley have already had offers of £1m and £1.5m turned down by the Baggies, and have returned with an improved bidof over £2m for the 24-year-old.
Boss Sean Dyche is determined to land the Rochdale-born defender, who left his hometown club in 2010 to join Albion for a fee believed to be in the region of £1m.
Dawson recently submitted a transfer request, which was subsequently rejected by West Brom, after struggling for first team opportunities at The Hawthorns.
He has made only 21 appearances in three seasons with the club - having spent a season back on loan at Rochdale, and the second half of the 2012/13 campaign in the Championship with Bolton Wanderers.
Dyche said on the latest developments: “There are a couple of things that are ongoing and a couple of fresh things that are just developing.
“It is a bit protracted with a couple of things, but sometimes that’s the nature of how it is, if you can’t throw money everywhere.”
Asked how many more players he would like to sign, on top of six arrivals so far, he added: “There’s not really a number on it.
“Obviously the Premier League has a 25-man squad situation so we have to look at that.
“But that doesn’t mean we have to have 25, we have to look at the financial numbers as well.
“There’s not a definite number but we just know that we still need more reinforcements at the moment.
“It’s a double edged sword, if things happen now, we want them to happen now, make no mistake.
“But if they don’t, it does allow you that time.
“Weird situations, good situations and not so good all open up in that last couple of weeks beyond the beginning of the season.”
Burnley kick-off their Premier League campaign a fortnight on Monday at home to Chelsea, but have until 11 p.m. on Monday, September 1st to sign players - with no emergency loan window in the Premier League.