Matic is out of contract in the summer, although United have the option to extend it for a further year, the Serbian admitted earlier in the season he is unhappy with his playing time.
The report states the Reds are long-term admirers of the England international who will have just 12 months remaining on his contract in the summer.
Dier has made just three substitute appearances in the last seven league games under Jose Mourinho and is without a league start since December.
Furthermore, the 26-year-old is a boyhood United supporter which could boost their chances of securing a deal though Spurs chairman Daniel Levy is known to be a tough negotiator.
United have targeted Dier in the past as the former Sporting Lisbon man Mourinho’s preferred midfield target in the summer of 2017, but he reunited with back-up option Matic instead.
Elsewhere, Paris-Saint Germain have been linked with a sensational swoop for United goalkeeper Dean Henderson.
The Englishman is currently spending his second season on loan with the Blades and has emerged as a contender for the England number one jersey at this summer’s European Championship thanks to his excellent displays in the Premier League.
With David de Gea signing a new contract at Old Trafford this season, he faces a tough challenge to usurp the Spaniard as United’s first-choice shot stopper.
The 22-year-old is currently spending a season on loan with Leeds United and has impressed under the tutelage of Marcelo Bielsa.
Football Insider claim the Foxes have been keeping tabs on his performances and Leeds have no option to buy the defender at the conclusion of his temporary spell.
United and Liverpool are the two other Premier League sides reported to be interested in the youngster.