Lundekvam joined Southampton in a £400,000 transfer from Brann in September 1996 and eventually left the club when retiring from football in May 2008.
During his long career with the Saints, the Norwegian defender claims he and unnamed team-mates made substantial sums of money by betting on events in games they participated in - a practice which is illegal.
"It is not something I'm proud of," Lundekvam is quoted as saying in The Sun. “For a while we did this almost every week. We made a fair bit of money.
"We could make deals with the opposing captain about, for example, betting on the first throw, the first corner, who started with the ball, a yellow card or a penalty. Those were the sorts of thing we had influence over.
“The results were never on the agenda. That is something I would never have done. We were professional competitors. Even though what we did, of course, was illegal, it was just a fun thing.”
The former Southampton defender alleged that attempts to spot fix were widespread during his time in English football.
“I know it happened at other clubs as well," Lundekvam said.
“We footballers live in a bubble. It was part of the lifestyle and the excitement. Whatever we could bet on, we bet on.”
FIFA has now said it will investigate the claims made by Lundekvam.
A statement said: "FIFA is monitoring this issue and involved its chief investigator in England. Once all information is known it will be decided who is leading the investigations."
Former Southampton forward Matt Le Tissier
claimed in his autobiography that he attempted to exploit the growth of spread betting by trying to kick the ball straight out of play during a game against Wimbledon in 1995. However, the attempt failed.