The left-back helped the Spanish outfit secure an impressive fifth-placed finish in La Liga under Manuel Pellegrini last season, which secured Europa League football for the 2022-23 campaign.
Betis also lifted the Copa del Rey trophy back in April to end their drought of over 20 years without silverware, with Moreno making 45 appearances across all competitions throughout the year.
The 29-year-old could now be set for a move to the Premier League however, with newly-promoted Fulham said to be close to securing his signature this summer, according to El Desmarque.
The report outlines how a bid of around €10m (£8.5m) has already been rejected by Betis, but that an offer of around €15m (£12.8m) will tempt them into a sale in the coming weeks.
That is an amount that the West London side are reportedly willing to pay for the Spaniard, and that a second offer will be on the table soon due to their serious interest in bringing him to the Premier League.
Marco Silva's side are due to offer Moreno a four or five-year deal with the club, where he would compete with the likes of Joe Bryan and Antonee Robinson for a place on the left-hand side of the defence should he complete a move.
Betis purchased Moreno for around £6.2m back in August 2019, where he has gone on to make 96 appearances for the club across all competitions so far.