Parejo's former Spain Under-20 colleague Oriol Romeu is already on Southampton's books.
The Spanish side are reportedly keen to overhaul their squad during the January transfer window, with Parejo one of six players made available for transfer.
Southampton are said to have watched the attacking midfielder for some time, and are keen to bring him to the Premier League.
However, the report adds that the Saints face competition from European heavyweights Sevilla, Inter Milan and Monaco.
Parejo reportedly came close to joining Sevilla in the summer.
The former Real Madrid player, who spent six months on loan to Queens Park Rangers in 2008, has scored three goals and created another five in 15 La Liga appearances this season.
The Daily Star reports that Parejo is valued at £16.7 million by Valencia, with whom he is under contract until 2020.
Parejo's former Spain Under-20 colleague Oriol Romeu is already on the Saints' books.
Young midfielders Harrison Reed and Jake Hesketh both agreed new contracts at St. Mary's on Thursday.
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