Both players are to begin trials this coming week in the hope of securing short term contracts at St Mary's.
Full back Xavier, who also spent some time at Liverpool, was released by German side Hannover earlier this season and has been on trial with Blackburn Rovers recently whilst midfielder Nyarko is also a free agent and was recently training with Middlesbrough.
"They're both free agents so those deals would be quite straightforward," said the players' agent Barry Silkman.
"Abel Xavier is the more straightforward dealof the two, if he proves his fitness he will be ready whenever Harry needs him."