The 29-year-old is currently in discussions over an extension to a deal which expires in the summer of 2016.
Routledge had featured for eight clubs in six years before joining the Swans in 2011, and Monk wants the Welsh outfit to continue to be the beneficiaries of the winger's best form for years to come.
"We are talking to Wayne and his representatives," Monk told reporters after watching his side comfortably beat Everton 3-0 in the third round of the Capital One Cup on Tuesday.
"He has found a home at Swansea and somewhere he can perform at a very good level.
"He's been one of the most consistent performers in my time as manager and hopefully we can get that contract sorted as soon as possible."
Routledge has scored 13 goals in 127 appearances for Swansea and has started their last 24 Premier League games.