Swift, previously of Chelsea, was the subject of an approach from Bramall Lane last season after entering the closing stages of his contract at the Madejski Stadium.
United manager Slavisa Jokanovic, who replaced Chris Wilder at the helm in May, has made a more defensive midfielder one of his top priorities during the January transfer window with two wingers also featuring on the Serb’s wanted list.
But members of United’s recruitment department continued to monitor Swift’s situation in Berkshire following Wilder’s departure, adhering to their policy of tracking the progress of potential targets over a period of time.
Despite reports Jokanovic could rekindle United’s interest in the 26-year-old if he is given permission to reprofile their squad, that now appears unlikely with Burnley, Wolverhampton Wanderers and Leeds all considering bids.
Swift’s contract is set to expire at the end of the campaign and, after registering eight goals and six assists in his last 17 Championship outings, there is an acceptance the trio’s top-flight status will make them more desirable destinations should Reading decide to sell.
Jokanovic, whose team are 18th in the table, are scheduled to face Veljko Paunovic’s team later this month. Barcelona winger Alex Collado is understood to be an option for United when the market reopens after coming close to joining before the August deadline. However the deal collapsed, with United suggesting Collado’s representatives had attempted to alter key points – a claim they disputed.