The club play in the Northern Premier League Premier Division, the seventh tier of English football, which is not affected by the World Cup break like Premier League clubs.
As a result of Norway failing to qualify for the tournament in Qatar, Haaland will be out of competitive action for around a month and talkSPORT reports that the non-league club have made an official proposal for a 28-day loan deal for the attacker.
The Robins manager Michael Clegg told the club's website, that 'it makes sense'.
"City aren't playing, and we want to help by keeping Erling fit. It makes more sense than him playing golf for six weeks," he said.
"We think he will be a great fit for us and would slot in with our squad dynamic really well."
Ashton are yet to receive a response to their audacious offer for the 22-year-old, who has scored 23 goals in 18 matches for the Citizens so far this season.