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The Blues will face their west Cumbrian opponents at Carlisle City's Gillford Park ground next Tuesday, November 17.
The game was originally due to be played on October 27 but had to be postponed because of a waterlogged pitch.
The clubs will now try again next week with a place in the quarter-finals of the county senior cup on the line.
The west Cumbrian side will take on Carlisle United at Gillford Park (Image: Mirehouse AFC)
United are expected to field a young side against their opponents from the Cumberland County League.
Speaking before the postponed tie, Blues head coach Rob Elliot confirmed to the News & Star that United's under-18s would represent United in the competition.
“Birchy and Dev [under-18s coaches Mark Birch and Jamie Devitt] are going to take the team,” Elliot said. “So it will be a young team, because of the games we’ve got and where the squad is at.”
Mirehouse got past Cockermouth in the first round to book their meeting with the Blues.
The United v Mirehouse tie is the last remaining second round game to be played.
Teams to have already booked their places in the quarter-finals include Penrith, Maryport Athletic, Whitehaven AFC, holders Carlisle City, Cleator Moor Celtic, Workington Reds and Unisun Athletic.
Kick-off next Tuesday will be 7.45pm.