UEFA's Club Competitions Committee has agreed to scrap the away goals rule, the UK Times reports.
The move could drastically change knock-out fixtures in European club competitions.
On Friday, officials reached the verdict in a meeting, but UEFA's Executive Committee will now decide whether to approve the change.
The away rule stipulates that if two teams are on the same aggregate after two legs, the side with more away goals progresses to the next round.
It has been a controversial feature of European competitions since 1965.
It has been credited by some observers with making the knock-out stages of the Champions League and Europa League exciting and unpredictable.
But many UEFA executives feel it is outdated and have agreed to do away with it.
They will now begin lobbying the Executive Committee to sanction it.