The 23-year-old scored 11 goals in 50 matches in all competitions last season as his side won the Ligue 1 title.
United have so far added defender Victor Lindelof to their squad as they attempt to improve on last year's sixth place in the Premier League.
"Manchester United is a great team and I would think about it," Fabinho said.
"If [Manchester United manager Jose] Mourinho invites me it would be very tempting," he told Brazilian television channel Esporte Interativo.
"But I would have to talk with my agent and Monaco to make the things right."
Fabinho joined Monaco in 2013 on loan from Portuguese side Rio Ave and made his move permanent in 2015, when he also won the first of four caps for Brazil.
But having claimed the Europa League, Mourinho is being linked with several players in order to build a squad capable of dealing with the added fixtures.
Tottenham's Eric Dier and Nemanja Matic at Chelsea have been linked with a move to Old Trafford, as has Real Madrid striker Alvaro Morata.
United have strengthened their backroom staff in hiring Juventus scouting manager Javier Ribalta, who was at the Italian club with Morata.
Ribalta worked on deals for Dani Alves and Sami Khedira while at Juventus, who have secured six straight league titles.

That is despite the result being an eight-month delay in Hearts passing into fan ownership.
Present owner Ann Budge had proposed delaying the repayment of her £2.5m investment to help fund the project.
Following a vote of foundation members, only 43 were against the proposal and 3,790 in favour.
Hearts said on their website: "We are absolutely delighted that the foundation members have given such a resounding vote in favour of the offer from Ann Budge.
"This significant milestone on the road to the 'new' Tynecastle once more demonstrates our collective strength."
Hearts hope to fund the new stand via £3m from club reserves, £2.5m from benefactor contributions, £0.5m from commercial contributions, which leaves a shortfall of £6m once the club adds a contingency for an increase in costs.
The Scottish Premiership club hope to build up further reserves and launch a new debenture scheme, but the delay of up to two years in the Foundation of Hearts buying Budge's stake will allow funds to go directly into the club in the meantime.
"Assuming contributions continued at today's levels, majority ownership would pass to FOH only eight months later than originally envisaged," Hearts have stated.
Full planning permission is still required from City of Edinburgh Council, but Hearts have already planned out the progress of the two-year project that will result in a stadium with a capacity up to 21,000.
To prepare for the building of the new stand, the buildings behind the current stand - the administration block, the shop and nursery - would be knocked down, with temporary facilities being provided during construction.
The temporary buildings will be occupied in October, with the demolition beginning the following month.
Construction of the new stand will start over and behind the current stand during next season before being completed during the 2017 close season.
A move to Manchester United "would be very tempting", says Monaco midfielder Fabinho, who has been linked with the Old Trafford club.
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Fans group the Foundation of Hearts has voted overwhelmingly in favour of helping to fund the Tynecastle club's new £11m main stand.