A number of top European clubs have taken note of Lenglets performances for Sevilla this season in La Liga and Europe.
The French U21 star impressed in Uniteds Champions League defeat to Sevilla in March and scouts from Old Trafford have been sent to Spain to monitor his progress.
Barcelona have registered interest in the centre-back, contacting Sevilla to enquire about the possibility of securing his services this summer.
But, according to The Sun, United are prepared to outbid Barcelona, both in terms of a transfer fee and a personal salary.
Lenglet has made impressive strides since signing from Nancy in 2017 and United believe he is a player who can flourish in the Premier League.
Jose Mourinho is said to be ready to reshuffle his defence this summer, with uncertainty over the long-term futures of Phil Jones, Marcos Rojo, Chris Smalling and Victor Lindelof.
The Red Devils, second in the Premier League, booked their place in a record-equalling 20th FA Cup final on Saturday with a 2-1 win over Tottenham.
Spurs took the lead at Wembley through Dele Alli before goals from Alexis Sanchez and Ander Herrera sealed the victory for Jose Mourinhos side.
Speaking after the win, Mourinho said: We deserve it. If we split the match into periods we were the best team for many of these periods.
Even when they had the ball when we were winning we were totally in control. We lost control after the 1-0.
At half-time we spoke – we came back late for the second half because we spoke a lot – and organised ourselves.
We should ask ourselves why there are too many critics on all of us? We can finish second [in the Premier League] by getting six points.
To do that with all the fantastic teams we play against will be an achievement for a club that couldnt do it for a few years now.
And it will be a fourth final in three years. So, maybe too much criticism.