Parker, 37, decided to retire from playing last summer, calling time on his career after turning out for Charlton Athletic, Norwich City, Chelsea, Newcastle United, West Ham United, Tottenham Hotspur and Fulham.
The midfielder decided to turn his hand to coaching, and made a return to Tottenham as Mauricio Pochettino handed him a role in charge of the Spurs Under-18's.
Parker is just one year into his coaching career, but he could already move on from North London after reported interest from Championship side Ipswich Town.
The Mirror report that Parker has held talks with Ipswich about becoming their new manager, with owner Marcus Evans keen to bring in a young, exciting manager to replace Mick McCarthy.
The Tractor Boys parted ways with McCarthy last month, and they must now find a replacement, with a host of options pursued – including rookie Parker after a recent interview.
Frank Lampard, Jaap Stam, Tim Sherwood and St Mirren's Jack Ross are also in the frame, and Spurs may well be hoping that Parker decides to stay with the club and help develop their young players.