The 23-year-old has asked to be traded to the Western Bulldogs, but the Swans have tried to trump the Dogs' offer by putting their first-round selection in the NAB AFL Draft (pick 21) on the table.
"We've spoken to Brisbane and obviously we've got a lower draft pick [than the Dogs]," Longmire said on Wednesday afternoon on afl.com.au's Trade Week Radio.
"We really rate Justin. We understand that his first preference is to get to Melbourne, but we still think there's a bit of water to go under the bridge yet."
The duel to secure Sherman is in contrast to the recent co-operation between the Dogs and Swans which saw Andrejs Everitt and Patrick Veszpremi trade places.
However, Bulldogs general manager of football operations James Fantasia remains confident Sherman will end up at the Whitten Oval.
"We're happy for Sydney to do their due diligence and try and talk to the player," Fantasia said.
"We expect them to do that and also talk to Brisbane, but at the end of the day the player has to agree to a deal.
"I can't speak for Justin, but he's certainly made it clear that he wants to come to the Western Bulldogs, and I think the selection we're offering up is only seven or eight different [to the one put up by the Swans].
"It shouldn't be too much of a sticking point from where we sit anyway."
Follow our complete coverage of the 2010 AFL exchange period from October 5-11. No trades are official until paperwork has been accepted by the AFL and formally recognised after 2pm on Monday, October 11.
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