Mignolet has shared goalkeeping duties with Loris Karius throughout the season but has managed just one appearance for Liverpool in recent weeks, a 3-2 loss to West Brom in the FA Cup.
It remains to be seen if Roma bow to Alisson's wish but their need to comply with Financial Fair Play could force them to listen to offers for the Brazilian in the summer, with Paris Saint-Germain and Real Madrid also believed to be interest in his services.
Summer signing Loris Karius has since filled his boots, starting the last five Premier League games and is expected to keep his place against Porto tomorrow (7.45pm).
Simon Mignolet has at times stamped his authority on the No 1 jersey but is prone to errors and was dropped by Jurgen Klopp last month. "I don't like to talk too much about it because we are only interested in the next game, but [his performance at Southampton] was important", enthused the gaffer.
"I really think Aguero and Kane and a few others are really good players as well, but our boys are important for us", the German boss added.
Asked about Mignolet, Klopp said at his news conference on Tuesday: "Nobody knows about future; or I don't know about the future". "To be honest I have not made the final decision but it is".
In the first half of the campaign, Karius played in Europe while Simon Mignolet had the responsibility for the Premier League.