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 spending 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, bought by The Abu Dhabi United Group in 2008, also sold several players over July and August, including Kelechi Iheanacho, Wilfried Bony and Aaron Mooy, leaving their net spend at about £130m.
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."
The Economic and Financial Crimes Commission (EFCC) yesterday interrogated former Governor of Akwa Ibom State Godswill Akpabio over allegation of financial crimes. Daily Trust gathered that Akpabio honoured the invitation by the anti-graft agency to explain allegations of looting of the state’s funds during his tenure. Sources told our correspondent that Senator Akpabio was being interrogated late yesterday evening at the Abuja head offices of the Commission. He was spotted at the EFFC office in company of a Senior Advocate of Nigeria, Rickey Tarfa, at about 5:20pm. Akpabio’s arrest yesterday is fallout of the petition by an Abuja-based lawyer and activist, Leo Ekpenyong, who had on June 8 this year petitioned President Muhammadu Buhari and the EFCC, calling for Senator Akpabio’s probe and accusing him of looting. The petitioner had earlier on Wednesday adopted his petition and provided more details to the anti-graft agency on the allegations against the minority leader of People...
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