The 22-year-old is regarded as a promising defensive prospect but found starts relatively hard to come by last term due to Nicolas Otamendi and Antonio Silva's effective partnership.
Morato scored once in 21 matches for the Eagles last season, but he only made seven starts in the Primeira Liga and also played just 106 minutes in the Champions League.
A sprained ankle also did Morato no favours, but Benfica still opted to tie the Brazilian down to a new contract in September, and those terms do not expire until the summer of 2027.
However, the Daily Mail claims that Fulham have now begun negotiations to sign Morato, who has been identified by Marco Silva as a strong candidate to beef up his backline.
Morato represented Sao Paulo at youth level and departed his boyhood club in 2019 in a €7.6m (£6.5m) deal for Benfica, where he has scored two goals in 50 games since earning promotion from the B team.
Meanwhile, Nottingham Forest are reportedly aiming to bolster their attack with the signing of Kelechi Iheanacho from Leicester City.
The former Manchester City man endured a frustrating season with the Foxes under Brendan Rodgers and Dean Smith, only starting 11 top-flight matches.
Iheanacho still managed to directly contribute to 10 goals in 28 Premier League contests - five of his own and five assists - but his efforts were largely futile as Leicester dropped down to the Championship.
The 26-year-old now has a little under 12 months left to run on his contract at the King Power Stadium, and according to Foot Mercato, Forest could offer him the chance to continue in the Premier League.
Tricky Trees boss Steve Cooper has reportedly identified Iheanacho as his top attacking target, and Forest are hopeful of wrapping up a deal within days after beginning talks with Leicester.
The Foxes paid €27.7m (£23.7m) to prise Iheanacho away from Man City in 2017, and the striker has since registered 55 goals and 33 assists in 206 matches for the club, winning the FA Cup and Community Shield in 2021.
Over at Turf Moor, Burnley are believed to be closing in on the signing of Borussia Dortmund's Soumaila Coulibaly on loan with an obligation to buy.
The 19-year-old left Paris Saint-Germain's academy in the summer of 2021 to join Dortmund on a free transfer and made his first two appearances for Edin Terzic's side last season.
Coulibaly made his Dortmund debut in a Champions League group-stage draw with Copenhagen, before playing the second half of a 3-3 Bundesliga draw with Stuttgart in April.
According to BBC Sport, Coulibaly - who is still under contract with Dortmund for another three years - is now on the brink of joining Premier League returnees Burnley on loan with an obligation to buy for £15m next year.
The 6ft 3in centre-back is reportedly set to complete his medical on Monday and will become Burnley's fifth signing of the summer after Lawrence Vigouroux, Dara O'Shea, Michael Obafemi and Jordan Beyer.
Coulibaly has represented France at various levels in youth football and has two caps to his name for the Under-20 national team, but he missed out on a place in their recent Under-20 World Cup squad.
Finally, Southampton are believed to be close to wrapping up a deal to sign Manchester City academy product Shea Charles.
The 19-year-old has been on the books with the Citizens since 2011 and made his first-team debut for Pep Guardiola's side last season after progressing through the academy ranks.
Charles was brought off the bench in his side's 1-0 loss to Brentford on the final day of the Premier League season, and his contract at the Etihad still has another four years left to run.
However, the Daily Mail claims that Charles is now set to complete an £11m switch to Southampton as a possible replacement for Romeo Lavia, who also left Man City to join the Saints last year.
Southampton have apparently beaten Borussia Dortmund, Schalke 04, Leicester and Leeds United to the signing of Charles, but as was the case with Lavia, Man City have reportedly negotiated a sell-on and buyback clause.
Primarily a defensive midfielder, Charles can also operate as a centre-back and full-back, and he has been capped on eight occasions by the Northern Ireland national team.