The £200,000-a-week midfielder is set to be available at the end of the season and United Boss Erik ten Hag is keen to add Reus to his squad.
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So much so that the Dutch tactician has already held talks with the 33-year-old's agent Dirk Hebel, according to Caught Offside.
Hebel was in attendance for last weekend's Manchester derby when United came from behind to beat Pep Guardiola's City 2-1.
The report states Hebel held talks with City but the reigning Premier League champions were put off by his age.
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Manchester United forward Anthony Elanga is admired by Dortmund and could be used as a makeweight should Ten Hag opt to sign Reus in January.
The Bundesliga side are keen to take Elanga on loan for the remainder of the season with his game time restricted at Old Trafford.
Meanwhile, Reus is open to a new challenge after spending 11 years of his career at Signal Iduna Park.
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Ambitious Saudi outfit Al-Nassr are also believed to be tracking Reus who could opt to line the Germany international up alongside Cristiano Ronaldo.
Reus is viewed as a legend in Dortmund after his arrival from Borussia Monchengladbach in 2012.
He has gone on to play 368 times for the club, netting 156 goals.
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Reus has been capped 48 times by Germany but missed the 2022 World Cup in Qatar after failing to recover in time from an ankle injury.
The midfielder has struggled with injury throughout his career which led to him missing Germany's 2014 World Cup triumph.
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