The Liverpool legend made the suggestion following France’s win against Romania at the Euro 2016 finals last week.
West Ham attacking midfielder Dimitri Payet was the star of the show for France at Stade de France in Saint-Denis in Group A on Friday evening.
The former Marseille star scored a goal and provided the assist for the other, as the home team won 2-1.
Carragher was following the match, and he was impressed with the performance of Payet.
The former Liverpool defender has jokingly suggested that Liverpool should try to get West Ham co-chairman Sullivan on their transfer committee.
WOW! Payet. Can we get David Sullivan on the Liverpool transfer committee?!!!— Jamie Carragher (@Carra23) June 10, 2016
Payet was one of the best players in the Premier League this past season. The France international attacking midfielder scored nine goals and created 116 chances in 30 league matches for West Ham during the 2015-16 campaign.