The Yorkshire Post understands the Tigers have lodged a club record bid with the Lancashire club for the Sheffield-born forward and are waiting for a response.
Davies, 31, has been at the Reebok Stadium for the past five seasons and is under contract until 2010, though his future with Wanderers remains unclear following the summer arrival of club record signing Johan Elmander from Toulouse for £11m and the club being linked with Israel international Elyaniv Barda.
Brown has made seven signings since Hull won promotion via the play-offs last May, but has so far been frustrated in his quest to bring in competition for Caleb Folan, Nick Barmby and Dean Windass.
Hull had a bid of around £3m accepted by Wigan for Marlon King late last month only for the deal to be held up by a dispute over the former Watford man's severance package.
King was a surprise starter for the Latics in their first domestic friendly of the year at Barnsley on Tuesday night when he netted the first goal in a 6-0 romp, his appearance sparking fears that the proposed move to the KC could be in danger of collapse.
Hull manager Brown remains keen on bringing Fraizer Campbell back to East Yorkshire following his successful loan spell, but is yet to hear whether Manchester United will allow the Huddersfield-born striker to return.
Sir Alex Ferguson indicated a desire to assess Campbell during pre-season, meaning the Tigers will have to remain patient despite the new campaign getting underway a fortnight tomorrow.
Meanwhile, Hull transfer target Abdoulaye Meite has been the subject of an improved bid from West Bromwich Albion.
The £1.5m offer has, however, been rejected by Bolton with the club understood to want around £2m for the defender.
A Wanderers source said: "The offer is derisory. Abdoulaye is a player with considerable Premier League experience. Gary (Megson) is not openly touting Abdoulaye for a transfer and will not let him go for anything other than market value."
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