Monk was appointed as interim head coach following the dismissal of Michael Laudrup last month.
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Lita made his first Premier League appearance of the season for Swansea in the 1-1 draw with Crystal Palace last Sunday, despite not being named in the latest edition of the 25-man squad last month.
However, the former Reading and Middlesbrough man is now available to play in the league for the remainder of the season.
Swansea have taken five points from Monk's first four league games in charge and succumbed to a valiant 3-1 aggregate defeat to Serie A side Napoli in the last 32 of the Europa League.