Gianni Infantino, the general secretary of European football's governing body, said the practice - which is already outlawed in the Barclays Premier League and France's Ligue 1 - could not be allowed to continue.
"This kind of player ownership is a growing threat," he told Bloomberg.
"We will ourselves look into this matter because it cannot continue in this manner."
Third-party ownership is allowed in Spain, Italy, Germany and Portugal.
Officials from England and France have already complained to UEFA that clubs could use such investments to circumvent Financial Fair Play regulations.
Infantino said he would "certainly look into" the possibility of banning third party-owned players from the Champions League and Europa League.
FIFA rules do not prohibit investors buying stakes in players, providing they have no control over when they can play or when they are bought and sold.
The Premier League is opposed to third-party ownership because they say "it threatens the integrity of competitions, reduces the flow of transfer revenue contained within the game and has the potential to exert external influences on players' transfer decisions".
They banned the practice in 2007 following the controversy over the transfers of Carlos Tevez and Javier Mascherano from Corinthians to West Ham.