In March, European football's governing body confirmed it was looking into claims of payments made by Barcelona for favourable refereeing decisions.
Barcelona have denied any wrongdoing.
While Barcelona have been allowed in Europe, Uefa reserved the right to punish the club in the future.
The Uefa investigation came after a criminal investigation was brought by the Barcelona public prosecutor's office on 10 March.
It was alleged that Barcelona paid 8.4m euros (£7.4m) to Jose Maria Enriquez Negreira, the former vice-president of Spain's referees' committee and his Dasnil 95 company.
Barca, former club officials and Negreira were indicted for "corruption", "breach of trust" and "false business records".
Uefa said: "The investigators in charge of the case are invited to continue and finalise their investigation and to send a further report to the appeals body if and when they consider that the admission/exclusion of FC Barcelona [in the Champions League] should be assessed."
The payments, revealed in February by radio station Ser Catalunya, came to light following an investigation by tax authorities into Negreira's company Dasnil 95.
Barcelona made payments to the company totalling a reported 1.4m euros (£1.2m) between 2016 and 2018, and paid Negreira, 77, about 7m euros (£6.2m) between 2001 and 2018, the year he left his role with the referees' committee.
Barca acknowledged the club had paid Dasnil 95, which it described as "an external technical consultant" to compile video reports related to professional referees "with the aim of complementing the information required by the coaching staff".
It added that contracting the reports was "a habitual practice among professional clubs".
The affair escalated when 18 of the 20 La Liga clubs issued a statement to express "deep concern" over the situation, and Barcelona president Joan Laporta said the club would launch an internal investigation into the payments.