Pochettino was brought to Stamford Bridge as a permanent replacement for Graham Potter, and the Argentine has fared better than his predecessor.
The Blues have reached an EFL Cup final, an FA Cup semi-final and currently remain in contention to secure qualification for a European competition through their Premier League position.
However, Tuesday's 5-0 defeat to Arsenal abruptly ended an eight-game unbeaten streak in the top flight and left the club as outsiders for seventh place.
While achieving continental football will not necessarily impact on Pochettino's future either way, meeting that target would be of a natural benefit.
Chelsea hierarchy yet to decide on Pochettino
According to The Telegraph, the Chelsea board have not reached a conclusive decision over how to act in the summer.
That is seemingly a consequence of their being positives and negatives to his reign, with pressure allegedly growing in some quarters over decisions he has made.
Nevertheless, there is also reportedly an acknowledgement that blame for Chelsea's inconsistencies should be shared, rather than solely attributed to the Argentine.
Pochettino is said to not have had a major voice in the conversations that took place over the makeup of Chelsea's squad, with young players with potential being targeted over experience.
Providing that Thiago Silva leaves in the summer as expected, the only player in the squad who is over 30 years of age will be 31-year-old third-choice goalkeeper Marcus Bettinelli.
Two managers willing to replace Pochettino
The report adds that Chelsea are not against taking the stable route and retaining Pochettino regardless of how they finish the campaign.
On the flip side, it is claimed that there are two notable unnamed managers who would be prepared to take over the reins if Pochettino was sacked.
Pochettino's immediate concern is trying to instigate a response to the humbling at the Emirates Stadium, which came three days after the defeat to Manchester City in the FA Cup semi-finals.
After the most recent game, Pochettino was outspoken about the poor performance, admitting that Chelsea had been "so bad" during the second half.
Chelsea next make the trip to the West Midlands to face fourth-placed Aston Villa on Saturday evening.