The former Tottenham defender is thinking about standing to replace suspended outgoing president Sepp Blatter in February’s elections.
Vice-president Michel Platini, a three-time European Footballer of the Year, is also banned amid corruption claims.
“If I am the catalyst to reforming Fifa then I’m definitely considering going forward,” said Swiss Vega, 44.
Fifa’s executive committee meets on Tuesday to discuss whether to postpone February’s presidential election.
Uefa president Platini, 60, says he has been treated “shamefully” and insists he will still stand, with Jordanian Prince Ali bin al-Hussein and former Trinidad and Tobago midfielder David Nakhid the other confirmed candidates.
Shaikh Salman bin Ebrahim al-Khalifa of Bahrain has yet to submit his candidacy, but claims “senior” figures in world football have encouraged him to enter before the 26 October deadline.
Asked by BBC sports editor Dan Roan if the time was right for a former player to become the new Fifa president, Vega replied “without a doubt”.
“I will definitely back a footballer to be leading a football association,” he said. “We are the product, we smell the grass, we smell the dressing room, we know the rules, the ins and outs, and the politics.”
Vega, who also played for Celtic and Watford during his time in Britain between 1997 and 2002, has worked in finance since retiring from football in 2004.
And he says he brings the “experience of two worlds of football and finance” to the table.
Vega told BBC Sport he has been approached by “various federations in Europe” to stand and will decide in the next few days.
The Football Association has suspended its backing of Platini pending the Fifa ethics committee’s investigation into an alleged “disloyal payment” from Blatter
Vega said he would welcome the FA’s backing and that it must be “a strong voice in the football world”.
Swiss Blatter, who is stepping down as president in February, is also under criminal investigation over claims he made a £1.35m payment to Platini in 2011, as well as allegations he signed a contract “unfavourable” to Fifa.
Both men deny any wrongdoing.