Laporta is hopeful that the 35-year-old will be able to return to Barca before he hangs up his boots.
According to many reports, the player will decide his future and put an end to this soap opera next Sunday.
Pochettino's position came under scrutiny after PSG were knocked out of the Champions League in the last 16.
Despite all the speculation that he will join Real Madrid as a free agent, the France superstar has insisted that his mind is not yet made up between moving to the Spanish capital and remaining in Paris.
Unhappy Paris Saint-Germain fans targeted the Argentine as well as Neymar during the 3-0 win over Bordeaux that followed the club's spectacular Champions League elimination at the hands of Real Madrid.
PSG, who lost the last-16 tie 3-2 on aggregate, did not immediately respond to a request for comment.
The France star has long been linked with a move to Madrid, who reportedly tabled an unsuccessful offer worth up to 180 million euros ($200 million) for Mbappe in August.
Neymar, who is under contract at PSG until June 2025, said he was more likely to play in the U.S. than return to his home country.
In the last minute of stoppage time, Mbappe burst into the box from the left and between two defenders before finishing past Courtois for his 22nd goal this season.
Messi has scored only two goals in Ligue 1 since his shock move to PSG last August after being forced to leave Barcelona after 21 years as the Catalans could no longer afford his salary.
The 34-year-old Messi was omitted from Argentina’s 27-man squad after not playing for PSG since Dec. 22 against FC Lorient in French Ligue 1.
Messi was among the four PSG players who returned positive results on Sunday.
The Argentine captain enjoys his best spell with the national team so far, having lifted the Copa America trophy last summer.
Messi suffered a knock on his left knee and an MRI scan earlier this week confirmed signs of a bone contusion. He missed PSG's 2-1 victory at Metz on Wednesday.
Messi suffered a knock on his left knee and an MRI scan earlier this week confirmed signs of a bone contusion.
The Egyptian had a breathtaking performance, leading his team to defeat star-studded Paris Saint Germain 34-31.
Making his first start for the French team, the Argentine forward hit the woodwork but was otherwise far from his brilliant best.
Messi is fit enough to play in Argentina’s World Cup qualifiers this week in spite of having played less than half an hour this season for his new club.
Pep Guardiola's City beat PSG in the semi-finals of last season's Champions League on the way to losing the final to Chelsea in Porto.
Kylian Mbappe is "relaxed" and not unsettled despite ongoing speculation about his future, Paris Saint-Germain coach Mauricio Pochettino insisted on Thursday.