Spurs sources have told Goal.com that the club are considering a number of candidates and are expected to interview more than one of the contenders - with Martinez top of their list.
The Wigan Athletic manager has his admirers in the White Hart Lane boardroom and is set to be formally approached after being made aware through third parties of interest from Spurs.
However, Tottenham are not expected to rush into making a quick appointment.
David Moyes is the favourite with most bookmakers but there is doubt among some senior Spurs figures about his suitability for the post, despite his decade of overachievement with Everton.
Rafael Benitez and Andre Villas-Boas will also be considered by the Spurs board, who are putting great store in the value of Premier League experience after having their fingers burned by the appointments of Juande Ramos and Jacques Santini.
Redknapp's dismissal was announced by Tottenham at 3.37am on Thursday following a night of legal talks to determine the compensation package payable by the club. It followed the irreconcilable breakdown of his relationship with chairman Daniel Levy.
Spurs now want a modern, dynamic manager who can make full use of the club’s magnificent new £40million training ground and develop a squad who have finished fourth in the league in two of the last three seasons.
When Redknapp was the leading candidate for the England job a few months ago, Spurs made progress in sounding out a number of potential replacements. Brendan Rodgers, who was appointed Liverpool manager last month, was the preferred choice.
Martinez, who, like Rodgers, is 39, held talks with Liverpool but made it clear that he was unwilling to work under the three-man team of executives planned by owners Fenway Sports Group.