The 19-year-old has made 19 league starts this season, scoring six goals, but is due to return to Anfield at the end of this term when his loan deal expires.
Martinez is confident he can persuade Anderson, who is due to feature against Bournemouth this weekend after a two month lay-off with a hamstring injury, and his parent club that a return to the Liberty Stadium would be the best option for the England U-19 international.
"We definitely want to keep Paul beyond this season and we'll do all we can to make that happen," Martinez told thisisswansea.co.uk.
"First of all we need to listen to what Rafa Benitez thinks, then we need to listen to Paul. We have made it very clear we'd like to have Paul here again next season, whether that's on loan or on a permanent basis."