Bennett, 66, who replaced Steve McNamara in February, says it could help England's preparations ahead of the 2017 World Cup.
The move would need approval from Super League clubs and the Rugby Football League (RFL).
"The clubs were broadly supportive of his ideas subject to gaining more details," said an RFL spokesman.
The RFL scrapped the traditional mid-season Test against France following a series of one-sided scores with the last one played in 2010 when England won 60-6.
It was replaced by matches against an Exiles side drawn from overseas players in Super League, but the fixture has not been played since 2013.
Brisbane Broncos boss Bennett, who will take charge of England at the 2016 Four Nations in October and November, also wants clubs to release players for a two-week training camp before the start of next season.
Meanwhile, Bennett has ruled out using St George's Park as a training base in the run-up to the Four Nations.
The RFL used the Football Association venue in the build-up to the 2015 Test series with New Zealand after previously basing the England team at Loughborough University.
England's new rugby league head coach Wayne Bennett wants the return of a mid-season international.