The clubs reported approaches at last week's FIFA-INTERPOL "Integrity in Sport Workshop" in New Delhi, and All India Football Federation (AIFF) vice president Subrata Dutta called it a genuine concern.
"Of course it is (a concern). Otherwise why would FIFA send INTERPOL here and spend so much money to educate us on how to tackle match-fixing, betting and other corruption?" Dutta told Reuters in a telephone interview.
"When FIFA is taking it so seriously, certainly it's a matter of concern and AIFF would look into it seriously.
"I have proposed the AIFF should have an anti-corruption unit headed by an integrity officer. The executive committee will discuss and decide on it.
"All clubs have been told to recognise, resist and report such approaches," he added without elaborating how many clubs were approached.
Early last year, Mumbai FC vice president Atul Bagdamia took a call from a Malaysian, promising the Indian club an all-expenses-paid trip to his homeland to play friendlies there.
Subsequently came the suggestion to fix I-League matches.
"When I got the hint, I said I'm not interested. I just put down the phone. I don't even remember the name of the person. He was a Malaysian," Bagdamia told Reuters.
Asked why he did not immediately report it to the AIFF, he said "I had refused the offer. I felt the matter ended there.
"They (AIFF) have now told us that they are going to appoint an integrity officer in the (anti-corruption) unit. That person has to be contacted for this sort of things in future.
"It will be much easier now. Everybody will know whom to contact, who is the right person. After the conference, there is lot of awareness. It's going to be much simpler and easier now."
Last month, five players and three team officials from a Malaysian lower league club were handed life bans after being found guilty of match-fixing.
In India, corruption has tainted cricket's image. Arrested with two other cricketers, former India fast bowler Shanthakumaran Sreesanth was been banned for life on spot-fixing charges last year.