According to a report by the Sun, the two clubs are currently monitoring the 22-year-old and could make a move for him in the coming months.
Declan Rice is valued at £100m by West Ham and has been the subject of transfer speculation in the past. The likes of Chelsea, Manchester City and Manchester United have all been linked with the England midfielder.
Although the Manchester clubs are reportedly in pole position to sign him, it remains to be seen whether they will match West Ham's valuation.
Rice came through the Chelsea academy but was released in 2014 at the age of 14 years. He went on to join West Ham's academy soon after and made his first-team debut on the final day of the 2016-17 season.
Since then, he has grown to become one of the most valued holding midfielders in the Premier League and has also become established on the international stage. He initially represented Ireland at international level but successfully switched his allegiance to England and has been an ever-present for the Three Lions.
Declan Rice was named West Ham's Young Player of the Year in successive seasons and also won the prestigious Hammer of the Year in 2020. It is widely believed that a move to a bigger club could be on the cards in the future and one of Manchester United or Manchester City could be his next destination.
Is Declan Rice needed more at Manchester City or Manchester United?
Fernandinho has been a loyal servant to Manchester City for almost a decade but the 36-year-old has precious few years left at the summit of the game.
In line with this, identifying a long-term replacement is of paramount importance at the Etihad and Declan Rice could be one of the players to fill the Brazilian's big shoes.
The Premier League champions, however, currently have Rodri on the books and the Spain international has performed admirably since his arrival from Atletico Madrid.
For Manchester United, doubts have been expressed about the performance of Nemanja Matic and Fred. Many believe that getting a holding midfielder is the last piece of the puzzle for the Red Devils to become the complete package.
A case can be made for both sides, although on current realities, Manchester United arguably have more need for a holding midfielder.