The Spanish football league wants Uefa to investigate whether Manchester City have broken financial fair play rules.
European football’s governing body is already investigating if Paris St-Germain have broken rules designed to stop clubs from ‘financial doping’.
La Liga president Javier Tebas said City and PSG’s “funding by state-aid distorts European competitions”.
However, BBC Sport understands Uefa has no intention of opening an investigation into City at this stage.
City and PSG spent hundreds of millions of pounds on new players this summer. Tebas said their spending “creates an inflationary spiral that is irreparably harming the football industry”.
PSG have been owned by the Gulf state of Qatar, via its Qatar Sports Investments fund, since 2011.
They more than doubled the world record transfer fee when they spent 222m euros (£200m) to sign Neymar last month, before adding Kylian Mbappe on loan from Monaco, a deal that is expected to be made permanent for £165.7m in 2018.
Manchester City’s summer spend of £215m was the biggest by any club in any transfer window and included deals for England full-back Kyle Walker (£45m), Portugal midfielder Bernardo Silva (£43m), Brazilian goalkeeper Ederson Moraes (£35m) and France defender Benjamin Mendy (£52m).
The Premier League club was bought by The Abu Dhabi United Group in 2008.
A La Liga statement released on Monday confirms it wrote two letters to Uefa on 22 August – one to express concerns over the French club, and another relating to City.
The body claimed that “both PSG and Man City benefit from sponsorships that make no economic sense and lack any fair value”.
The statement continued: “La Liga calls on Uefa to proceed with its investigation, taking into account the full history of PSG’s actions. Additionally, La Liga calls on Uefa to open a similar investigation into Man City.”