Hamilton, yet to agree a new deal with Mercedes beyond this year, started his career at McLaren and won the title in 2008.
"There isn't a team in the pitlane that wouldn't be interested in having Lewis drive for them, us included," team executive Brown told reporters.
Brown said that it would not even be a problem to revive the Hamilton-Fernando Alonso pairing that was so fiery in 2007.
"Fernando would have anyone as his teammate," Brown insisted.
Hamilton, however, would baulk at re-joining McLaren if the team's performance is not significantly better than it has been since 2015.
Brown, admitting that the similarly Renault-powered Red Bull's budget is bigger, said: "We should be the team that has the biggest improvement from last year to this year.
"If we are a second behind Red Bull, that will not look good, I agree.
"Perhaps we don't have the advantage of looking at as many car concepts as they can, but we do not believe we have any excuses or disadvantages."
Brown added that Renault are similarly confident heading into 2018.
"There are no alarm bells," he said. "They seem to be very confident and happy about where they are in terms of power and reliability."
The new season begins with the Australian Grand Prix on March 25.