The Toffees are set to undermine their Merseyside counterparts.
The 24-year-old has been a coveted target for several clubs this summer and has already turned down moves to both Bayer Leverkusen and Norwich City.
Alderweireld plays a similar role to current Toffees man Johnny Heitinga, in the sense that the Belgian is primarily a centre-back but is equally as adept at right-back.
The defender’s club have confirmed that Martinez’s team have shown interest in the the player, which suggests Heitinga could be on the way out at Goodison Park.
“It is true that Everton came forward for Alderweireld,” the Belgium international’s agent Soren Lerby admitted.
“Though there are other obstacles. Toby must now look at which team he thinks offers the best challenge.”
Alderweireld is a product of the Ajax youth system and made the step up to the first team in 2009, going on to play 183 matches in all competitions for the Dutch champions to date.
The defender has helped the Amsterdam outfit to three successive Eredivisie titles in the past three years and has also earned 25 caps for Belgium.
Alderweireld is a member of the current crop of talented players coming out of the country, which also includes a host of Premier League stars including Everton pair Marouane Fellaini and Kevin Mirallas.
The centre-back also has a significant amount of experience in European football having played in both the Champions League and Europa League with Ajax, which included beating Manchester City 3-1 last season.