talkSPORT reported last month that Ward-Prowse would be allowed to leave Saints in the event of them being relegated, which was confirmed last week.
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According to the Evening Standard, Ward-Prowse could be drafted in as a replacement for Rice, who has been heavily linked with move to Arsenal.
The report claims Moyes is eyeing up to two midfielders as he aims to fill the void which would be left by the England international's departure.
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It would be a huge blow if West Ham are to lose the 24-year-old given he is a mainstay in their side, missing just one league game all campaign.
However, Moyes admitted himself that there's a 'good chance' Rice will leave the club.
The report adds West Ham were keen on Ward-Prowse last season, but instead secured the services of Lucas Paqueta from Lyon and former Swansea star Flynn Downes.
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The 28-year-old's expertise from dead ball situations is something which particularly makes him an asset.
The Portsmouth-born midfielder joined Southampton at the age of eight, and has made 407 appearances so far, netting 54 goals.
The Saints' captain has previously also attracted interest from Tottenham and West Ham and also has admirers at Newcastle.
Remaining in the Premier League is certainly a necessity, as he looks to earn a place in Gareth Southgate's England squad for Euro 2024 next year.
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Manuel Lanzini is another player expected to leave, with a move back to his homeland joining River Plate likely.