Putellas, 29, missed most of last season with an anterior cruciate ligament injury, but she returned for the final six games of the campaign and has been named in Spain's squad for this summer's Women's World Cup.
However, with one year to run on her contract, which expires in 2024, some reports had suggested Barca would be open to letting her go after winning the Champions League without her this season.
"With Alexia, we are quite close to reaching an agreement to renew her contract," Laporta told La Vanguardia, knocking back suggestions offers would be entertained for the club captain.
Putellas's role in Barca's success over the last few seasons has earned her two Ballons d'Or and two Best FIFA Women's Player awards in the last two years.
An ACL injury picked up ahead of last summer's European Championships in England ruled her out for 10 months, but did not slow down Barcelona's progress on the pitch.
Without Putellas, Barca sealed a fourth consecutive Spanish women's league title and won the Champions League for just the second time in their history, coming back from two goals down to beat Wolfsburg in the final.
Putellas did come off the bench for the last few minutes of that final, but Barca's success in Europe, coupled doubts about how she will return from injury and the club's need to make cutbacks across the board, led to Spanish radio station Cadena Ser reporting at the start of June that the midfielder was no longer indispensable.
In her first start for her country in a year, she scored in last week's win over Panama as Jorge Vilda's side stepped up preparations for the tournament in Australia and New Zealand from July 20 to Aug. 20.
"The plan was for her to play 45 minutes, but she felt good and she reached 60," Vilda said after the game. "I know she would have [wanted] to play the whole game, but I don't want any risks.
"Beyond the goal, her performance was really good, but the best Alexia is still to come."