The new manager has won all three of his competitive games at Spurs, most recently beating Queens Park Rangers 4-0 on Sunday.
Pochettino came up against former Spurs boss Harry Redknapp, who was sacked by the north London side after three and a half seasons in charge.
Pochettino, however, could be around 'for a while,' according to Lineker.
Indeed, the former Spurs and England striker thinks the Spaniard is a 'fine, tactically astute' manager.
Spurs have got themselves a fine manager in Mauricio Pochettino. This fella might actually be around for a while. Tactically very astute!— Gary Lineker (@GaryLineker) August 24, 2014
“@Lord_Sugar: You do know words can haunt you. I know a chap who said you'll win nothing with kids. < Oh yes. But no one likes a know it all— Gary Lineker (@GaryLineker) August 24, 2014
Lineker even got a reply from former Tottenham chairman Sir Alan Sugar, who prefers to remain cautious after Spurs' recent history.
After Redknapp left White Hart Lane, the club sacked Andre Villas-Boas after just one and a half seasons at the club, with his replacement Tim Sherwood also leaving after a brief stint.
In Pochettino, though, Tottenham fans will hope they have a manager that can last. So far, as Lineker says, so good.
Will Pochettino last at Spurs?