Barca have already completed the signing of Eric Garcia on a free transfer from City this summer but coach Ronald Koeman would also like to add another more experienced centre-back to his squad.
However, the La Liga side have six defenders on their books and would need to shed two before even thinking about making a move for Laporte, who is at Euro 2020 with Spain.
Even without the addition of a new centre-back, Barca are keen to get Umtiti off the wage bill this summer.
The France defender could not get into the team last season after returning from a persistent knee injury but Barca are struggling to find a club willing to take on his salary.
If Umtiti does leave, Barca would still have to move on another centre-back before thinking about Laporte, with Lenglet someone they would consider offers for.
Lenglet, a €35.9 million signing from Sevilla in 2018, said earlier in June that he does not see himself leaving Camp Nou this summer.
Laporte joined the Premier League side in 2018 from Athletic Bilbao for his €65m release clause. He has made 111 appearances for the club.
Laporte's fee could also be a stumbling block for Barca, although president Joan Laporta said Wednesday the club will look to player exchanges to make more signings this summer.
"There will be more signings, but not normal signings, given we're not in [a good financial] condition," Laporta said.
"We will find the formula to respect the [Financial Fair Play] rules and try through exchanges, with the complicity that entails with other clubs."