UEFA says it opened investigations against Liverpool and Inter Milan for overspending and possible breaches of Financial Fair Play rules.
The former European champions are among seven clubs being investigated for "break-even deficits" in the past two financial years.
UEFA says Monaco and Roma, both former runners-up, are also implicated, and must provide extra financial reports in the next two months.
All four clubs are being closely scrutinized on returning to the Champions League this season.
Their finances were not assessed last season when UEFA started punishing clubs for overspending.
Sporting Lisbon, Besiktas and Krasnodar complete the seven-club list.
UEFA says a further five clubs have had their prize money from this season's Champions League or Europa League withheld because of unpaid wages, transfer fees or taxes.