The attacker and goalkeeper have been linked with moves away from Spurs in recent months, amid talk that they are both unsettled.
Lamela was only snapped up by the Londoners in a club record deal last year, but a series of niggling injuries and an inability to adjust to life in England has led to talk that he is eyeing a return to Serie A – where he starred for Roma.
Lloris has also been linked with a switch away from the club in search of Champions League football, after growing frustrated with two consecutive season that have not yielded qualification for a spot at Europe’s top table.
However, Pochettino wants to keep the pair.
The Argentine – who recently took the role in the Spurs dugout after impressing at Southampton – is beginning to formulate his first-team plans, and is keen to ensure that the stopper and the attacker stay put.
There is a hope at the club that Lamela will come good under the guidance of his compatriot, yet there have been suggestions that offers of around £20m may be accepted, which has alerted Inter Milan and Napoli.
Lloris is a player Pochettino is thought to admire following his impressive two seasons in the Premier League, where he has developed a reputation as one of the division’s top ‘keepers.