New Spurs boss Mauricio Pochettino wants Janmaat to add competition for the right-back spot with Kyle Walker at Tottenham next season, potentially ending Naughton's time at White Hart Lane.
According to reports, Spurs have already made contact with Feyenoord over a possible transfer for the Dutchman, who is also a target for Napoli and Manchester United.
Janmaat's arrival would add quality to the Tottenham defence, and the 24-year-old is one of a number of fullbacks that Spurs are chasing this summer.
Kyle Naughton would likely leave the club as he would be surplus to requirements, despite playing several games towards the end of last season in place of the injured Walker.
The 25-year-old joined Spurs from Sheffield United in 2009 in a deal that also saw Walker make the switch, but he has played second-fiddle to his teammate during his time in North London.
Naughton didn't register a goal or an assist last season, whereas Walker scored one and got two assists, though the two were closely matched statistically in several key areas.
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Naughton won more tackles per game, and surprisingly entered the final third of the pitch more often than Walker last season.
Though the first-choice right-back remains to be Kyle Walker who outperformed his long-time teammate in terms of both passing and crossing accuracy.
Feyenoord would demand £6 million for Janmaat, who is known to get forward, something Spurs fullbacks are encouraged to do and would certainly fit the system.
Janmaat scored twice and got five assists in his 30 Eredivisie appearances with Feyenoord last season and would be a solid acquisition if he were to make the switch.
The Dutchman who is heading to the World Cup with the Netherlands won more tackles per game (2.20) than both Naughton and Walker, and would certainly add stiff competition to Kyle Walker's starting berth at the club.