The Poland international was linked with a move to Saudi Arabia during the summer, but it is believed that he made it clear that a switch away from Camp Nou at this stage of his career was not in his mind.
The 35-year-old arrived at Barcelona from Bayern Munich last summer, and he impressed during his first season at the club, scoring 33 goals and registering eight assists in 46 appearances.
Lewandowski has also been in strong form this term, netting six goals and registering four assists in nine appearances, with five of his goals coming in Spain's top flight.
The centre-forward has another three years left to run on his contract at Barcelona, but he is entering the latter stages of his career, and according to Sport, several teams in the Saudi Pro League are determined to push for his signature in 2024.
The report claims that Barcelona are not planning to sell him next summer, but the situation could change if Lewandowski makes it clear that he wants to seek pastures new.
As one of the leading players in European football, the Pole would be capable of commanding a huge salary in Saudi Arabia, with any deal likely to put him among the top earners in the Saudi Pro League.
Abha Club are believed to be one of the Saudi teams keen on his signature, while more are likely to join the race if it becomes clear that he will be on the move next year.
Lewandowski has managed 39 goals and 12 assists in 55 appearances for Barcelona, following on from the 344 goals and 73 assists that he registered in 375 matches for Bayern.
The forward played the full 90 minutes of Barcelona's 1-0 victory over Sevilla in the league on Friday.
Lewandowski is now preparing for the Catalan outfit's second match of the 2023-24 Champions League group stage away to Porto on Wednesday night.
Barcelona currently have three players on the treatment table, with Pedri missing due to a thigh issue, while Frenkie de Jong is unavailable for selection due to an ankle problem.
Raphinha is also facing a spell on the sidelines with the hamstring injury that he sustained in the narrow success over Sevilla.
Barcelona remain unbeaten in all competitions this season, posting seven wins and two draws from their opening nine games of the campaign.