Josh Brownhill was Burnley's captain last season as they achieved promotion back to the Premier League.
The midfielder was influential for Scott Parker's side, scoring 18 goals, with six assists in 42 Championship matches.
However, he left the Clarets following the expiration of his contract, and now his career in English football is set to come to an end.
James Savundra of Sky Sports posted on X: "Brownhill is considering a huge offer from Al Shabab. Saudi Pro League side willing to pay upwards of £100K per week.
"Has held discussions with two Premier League clubs Leicester, Southampton & Ipswich expressed interest."
Al-Shabab is an ambitious Saudi Pro League side
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Many top players have left playing at the highest level in Europe for the Saudi Pro League.
The finances that clubs in Saudi Arabia can offer make a move to the division difficult to spurn.
Al-Shabab finished sixth in the Saudi Pro League last season and is looking to push on from this.
Long-term Real Sociedad coach, Imanol Alguacil, is Al-Shabab's manager.
Notable players in their roster include former Wolves player Daniel Podence and ex-Atletico Madrid midfielder Yannick Carrasco.