The Saints boss is in talks over a new deal according to reports, which suggests the club may be hopeful of reaching a conclusion before the end of the season.
Pochettino, 42, had initially vowed in the summer of 2013 that if Nicola Cortese were to leave Southampton that he would follow suit. However, following Cortese's departure, the Argentine decided to remain at the club but admitted that he would review his position at a later date.
It is thought that club owner Katharina Liebherr is keen to ensure that Pochettino remains at the club beyond the current season, as she prepares a boardroom shake-up. Liebherr is reportedly set to appoint three new board members, including former NHL coach Ralph Krüeger this summer.
No immediate plans to sell the club appear to be in place, nor does there seem to be any desire to sell the club's biggest assets, namely Luke Shaw and Adam Lallana.
Pochettino described Southampton as 'a project' upon joining the club, and will have been seeking assurances on the path that the club will take after the exit of Cortese.
The Telegraph claims that Pochettino and Southampton are in 'advanced talks' about a new deal for the former Espanyol boss, whose current deal expires in 15 months' time.
In addition, it is also claimed that Pochettino currently earns in the region of £1million a year and Southampton are prepared to offer him a considerable advance on that figure in light of his work.
Pochettino arrived at Southampton in January 2012 having replaced Nigel Adkins. The club were 15th at that time and finished the season in 14th having avoided relegation with crucial home wins over Liverpool, Manchester City and Chelsea.
This campaign sees the Saints in 9th position entering the closing stages of the season, with 8th place still a realistic target and 7th place not beyond the realm of possibility. The additions of Dejan Lovren and Victor Wanyama have proved important for Southampton, who in the opening ten games of the season had the second-best defensive record in Europe.
While the future of the club still appears somewhat uncertain, Pochettino's willingness to discuss and potentially sign a new deal should come as a welcome message of reassurance to the club and its fans with regard to the ambitions and level of investment that Liebherr is prepared to commit to the club.