Sokratis missed Tuesday’s 2-2 draw with Chelsea because of illness but he is expected to recover for the FA Cup fourth-round tie.
Luiz is banned against Bournemouth following his red card at Stamford Bridge and midfielder Granit Xhaka had to play three-quarters of the game at centre-back.
Shkodran Mustafi is the only other centre-back option available to Mikel Arteta, so the return of Sokratis would be a major boost.
Arteta is expected to name a strong side against Bournemouth, with Gabriel Martinelli set to start following his brilliant solo goal against Chelsea.
Arsenal are targeting a move for Paris Saint-Germain left-back Layvin Kurzawa, who is valued at £4million.
Kurzawa is out of contract at the end of the season and PSG are willing to let him leave this month.
Bukayo Saka has impressed as an emergency left-back and Hector Bellerin made a goalscoring return against Chelsea but Arteta is keen to bolster his full-back options.