Welsh Rugby Union chief executive Martyn Phillips hopes Anthony Joshua's next fight will be held at Cardiff's Principality Stadium.
Joshua lost his world IBF, WBA and WBO titles to Andy Ruiz Jr on 1 June.
The Londoner can insist on a rematch later this year.
The Cardiff venue has the only retractable stadium roof in the United Kingdom and Phillips said: "We'd like to think if it's in the UK we'd be in with a shout for that."
Joshua's promoter Eddie Hearn has said if the the rematch happens, it will take place in November or December, 2019.
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Wales host Barbarians on 30 November at Principality Stadium in a rugby match so the Joshua v Ruiz Jr bout would have to accommodate that.
Phillips said as stadium owners the Welsh Rugby Union would "certainly love to" see Joshua in action there again.
The Londoner stopped Carlos Takam in Cardiff in October, 2017 and beat Joseph Parker a the same venue the following March.
"We know he likes fighting here," said Phillips.
"Obviously he's had some success here over the last couple of years so if the fight does happen at the end of the year, we'd like to think if it's in the UK we'd be in with a shout for that."