The Man City treble winner, 28, is a shock contender to swap the Premier League for the Gulf state.
Silva would be by far the biggest scoop for the Saudi Pro League, a player in the prime of his career.
It has been mostly ageing stars who have opted to join Cristiano Ronaldo in the Middle East this summer.
Karim Benzema is arguably the biggest name to have joined forces, signing for Al Ittihad from Real Madrid on a three-year deal.
Chelsea's N'Golo Kante has also followed fellow countryman Benzema to the Saudi side, with Ruben Neves moving from Wolves to Al-Hilal at the age of 26.
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Kalidou Koulibaly is another player expected to leave Stamford Bridge joining Neves at Al-Hilal.
However, Carragher fears for players in their prime could be a 'game changer'.
"Bernardo Silva is in his peak years & has been one of the best players in Europe for the last five years!" Carragher wrote on Twitter.
"I wasn't worried about the Saudi League taking players in their 30's, a touch worried with players below the elite (Neves) but if this happens it feels like a game changer.
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"Saudi have taken over Golf, the big Boxing fights & now they want to take over football!!This sports washing needs to be stopped!"
Carragher's fellow Sky Sports pundit Gary Neville has already called for an embargo on moves from Premier League clubs to the Saudi Pro League.
Neville believes the source of the money funding the deals needs to be identified.
"The Premier League should put an instant embargo on transfers to Saudi Arabia to ensure the integrity of the game isn't being damaged," Neville told BBC Sport.
"Checks should be made on the appropriateness of the transactions.
Other players linked with a move to the Gulf Kingdom, include Chelsea trio: Edouard Mendy, Hakim Ziyech, and Pierre-Emerick Aubameyang.
Romelu Lukaku, Tottenham's Son Heung-min, Real Madrid star Luka Modric, Atletio Madrid's Saul, Inter Milan's Marcelo Brozovic, and former Barcelona midfielder Sergio Busquets, are other names linked.
While there has also been credible interest in Crystal Palace forward Wilfried Zaha and Paris Saint-Germain's Neymar.