Davies has helped Town to a league-leading 16 clean sheets this season and Alexander is desperate to hang on to his number one.
Fleetwood can exercise a one-year option on his current deal, which would keep the former Morecambe keeper at Fleetwood until the end of the 2013-14 season.
But Alexander wants to make sure his best players, Davies among them, commit to the club.
He said: “Scott’s contract isn’t up at the end of the season.
“There’s an option for another season, we’ve got that on our side.
“But we’re in talks with Scott, as we are with several other players.
“We want to get those people secured - to make sure those people who are doing a job for us are going to stay with the club.”
Davies this week told The Gazette work was going on behind the scenes on new contracts - Nathan Pond having already signed a new two year deal.
He said: “You want to get things sorted early, at the end of the day we’ve got mortgages to pay and families to feed.
“There’ll be plenty going on behind the scenes right now to sort new deals - that’ll be happening at clubs all over the country.
“But our focus has to stay on the pitch.”
Away from contract talks, Alexander is keen to arrange a friendly fixture in the coming week to help Youl Mawene and Andy Mangan with their ongoing recovery.
He said: “We want to try and get something sorted for Youl and Andy, we need to get them game time.
“We’ll be looking to set up a friendly, a reserves game, if we can to help them back.”
Town travel to Plymouth Argyle today, looking to build on Tuesday night’s victory over Accrington Stanley.
And Alexander is hoping Fleetwood can build on Jon Parkin’s Tuesday night hat-trick, which ended a run of one goal in four games.
He said: “Jon had four chances and took three of them. David Ball could have scored and Jean Michel Fontaine hit the bar at the end.
“It’s what you want to see.
“We treat every game in isolation but Accrington is encouraging.
“It’s good to be creating those chances because, at the end of the day, it’s strikers you win you games.”