The former France international refused to comment on Thursday after the home side came back from 2-0 down to win 3-2 and secure their Premier League status.
Vieira was surrounded by jubilant Everton fans celebrating the Merseyside club's last-gasp winner.
Merseyside Police said in a short statement that they had begun a probe into the events at Goodison Park.
"We are working with Everton FC to gather all available CCTV footage and are speaking to witnesses," the force said.
"No formal complaint has been received and enquiries into the incident are ongoing."
Thursday's pitch invasion came on the same day a Nottingham Forest fan was jailed for headbutting Sheffield United captain Billy Sharp after Tuesday's Championship play-off semi-final, the second leg.