According to a report from Estadio Deportivo, the two Premier League sides are chasing the 28-year-old midfielder, who is in his third season with the La Liga outfit.
Real Betis are in desperate need of balancing their books this summer, with the pandemic impacting them very negatively, leading to financial struggles.
Apart from Carvalho, Betis are also set to sell their other high profile players, such as Emerson Royal, Nabil Fekir and Aissa Mandi.
Carvalho's current contract at Betis is set to end in summer 2023, and Betis will be keen to sell him in the summer in order to get some sort of transfer fee for the midfielder.
Whilst he helped Betis to tenth-placed and fifteenth-placed finishes over his first two seasons in Spain, the club is currently in sixth and pushing very strongly for a UEFA Europa League spot.
However, Carvalho has struggled recently, having suffered from a muscular injury since the start of the year, with his last start in La Liga being back in December.
The former Sporting CP midfielder would be a great acquisition for either Wolves or Leicester, with the two sides wanting an experienced player in midfield.
Wolves in particular are in need of some depth in defensive midfield, with neither Ruben Neves nor Joao Moutinho being the defensive enforcers that the likes of Carvalho is.
The only player to fit that bill would be Leander Dendoncker, yet he has often been deployed in defence due to injuries in the back-line.
Leicester might have the likes of Wilfred Ndidi to fit in that position, but the likes of Nampalys Mendy and Hamza Choudhury have struggled to fill in that void when Ndidi has been unavailable, with Choudhury in particular being set to leave the club in the summer.
Carvalho has played in 21 La Liga games this season, and he is currently valued at around €15 million, a fee that would be attractive for both Wolves and Leicester.