Chelsea, Liverpool and Newcastle United reportedly all saw approaches for Inter Milan midfielder knocked back during the summer transfer window.
Despite establishing himself as one of the Nerazzurri's most integral players over the past couple of years, Barella's future at San Siro has often been a subject of debate.
The Italy international - who also shone during the Azzurri's run to Euro 2020 glory - most recently extended his Inter deal in 2021, and those terms are due to run out in just under three years time.
However, owing to his eye-catching record of 20 goals and 44 assists in 190 games for Inter, a transfer to the Premier League has been mooted for Barella for some time.
According to CaughtOffside, all of Chelsea, Liverpool and Newcastle tried their luck at a deal for Barella this summer, but each member of the English trio failed to prise him away from San Siro.
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Inter reinforced their midfield with a trio of notable signings in the summer window, bringing in Davy Klaassen and Kristjan Asllani on permanent deals, while taking Davide Frattesi on an initial loan from Sassuolo.
Inzaghi's side were also pushing to sign Lazar Samardzic from Udinese before a deal collapsed, but the report adds that the Nerazzurri will likely try again for the Serbian's signature in January.
Should Inter manage to wrap up a deal for Samardzic at the second time of asking, the Nerazzurri could supposedly be open to cashing in on Barella in 2024, and there is a growing feeling that he will end up in the Premier League.
However, the Italian giants are supposedly still prepared to demand around £77m to let Barella leave next year, which may prove problematic for the interested trio given their respective summer outlays.
After conceding defeat to Real Madrid in the race for Jude Bellingham, Liverpool brought in a quartet of new midfielders in Ryan Gravenberch, Alexis Mac Allister, Wataru Endo and Dominik Szoboszlai, but Thiago Alcantara sis expected to depart in 2024.
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Meanwhile, Chelsea stole Moises Caicedo and Romeo Lavia from under the Reds' noses, as well as continuing their youthful recruitment drive with the addition of Lesley Ugochukwu and Cole Palmer from Rennes and Manchester City respectively.
Newcastle did dip into the Serie A market to bolster their engine room, but the Magpies instead did business with Inter's San Siro rivals AC Milan to bring Sandro Tonali to St James' Park.
Despite the increased competition for minutes, Barella has started all three of Inter's opening 2023-24 Serie A games with Monza, Cagliari - whom he used to play for - and Fiorentina, which the Nerazzurri took a maximum nine points from.
Barella also played his part in helping Inter keep three clean sheets, but he was hooked before the hour mark against Fiorentina on September 3, having been booked on the stroke of half time.
The 26-year-old has won one Serie A title, two Coppa Italias and two Supercoppa Italianas with Inter, as well as starting 12 successive Champions League games during their run to the final last term.
