City have already turned down one official bid since New Year's Day for Wells, whose stock has continued to rise this season following the club's promotion to Sky Bet League One.
The 23-year-old has scored 15 goals in 21 appearances for Bradford this season and a long list of clubs, including several from the Barclays Premier League, have been linked with the Bermuda international.
Bradford manager Phil Parkinson said this week that he hoped the situation would be resolved quickly and Lawn told Press Association Sport: "It will be done during the early part of the transfer window, if it's going to happen.
"We want the market value for our leading goalscorer and as it stands we're negotiating with another club.
"Nahki Wells wants to go - that's what you have to get your head round.
"Whether we'll be using the money to strengthen this year or next year is down to Phil.
"What we won't be doing is wasting the money, if the right replacement is not available at the right price we won't be spending it."
Wells joined Bradford on a free transfer following his release from Carlisle in June 2011 and fired 26 goals last season as Parkinson's side reached the Capital One Cup final and secured promotion to League One.
Peterborough had a seven-figure bid for Wells turned down in the summer, while Bradford's Yorkshire rivals Leeds and Huddersfield, plus Reading, QPR and top-flight clubs Sunderland, Aston Villa and Stoke have all been linked with the forward.
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