The informal notification, expected to be followed by a detailed notice within a week, is the first outward sign of OPEC member Venezuela enforcing its share of the group's 2.2 million barrels per day (bpd) output cut agreed two weeks ago.
Saudi Arabia and the UAE have already informed customers of deeper export limits.
"They (Venezuela) have said we have to cut production. By how much...is not known to us. It will come shortly. But they have informed us," an official at ONGC Videsh, the Indian firm's overseas investment arm, said.
Oil prices slightly trimmed earlier losses after the news on Tuesday, but were still down 44 cents at $39.58 a barrel by 1111 GMT, ending a two-day rally and still struggling to put a floor under the collapse from a record $147 six months ago.
The source, who declined to be named because of company policy, said some form of formal communication was expected to reach ONGC in a week's time. A spokeswoman for ONGC Videsh declined to comment on the issue.
While the 30,000 to 35,000 bpd field is tiny compared with Venezuela's overall production, the step is important as some analysts had questioned whether OPEC members such as Venezuela and Iran -- which need to maximise oil revenues to balance their budgets -- would fully comply with the restraints.
Venezuela, which has historically pumped consistently in excess of its OPEC production limits, is due to cut output by about 350,000 bpd from November levels to 1.99 million bpd under the curbs due to take force from Jan. 1.
ONGC has a 40 per cent stake in the San Cristobal oilfield while Venezuelan national oil company PDVSA owns the remaining 60 per cent through its subsidiary CVP.
Compliance with OPEC's cuts -- including this month's biggest ever -- have become a key issue for oil traders who question whether the Organization of the Petroleum Exporting Countries can slash production quickly enough to keep pace with the decline in global fuel demand.
Early signs on supply in December, before the latest curbs came into effect, appear encouraging for the group. Output from OPEC members bound by supply constraints fell by 400,000 bpd this month, consultant Petrologistics said on Tuesday, as the group more than complied with its previous cuts.
Petrologistics estimated that Venezuela's output remained steady at 2.32 million bpd, while Saudi Arabia and the UAE led the curbs.
Riyadh informed its customers early this month that it would deepen supply curbs even further in January, effectively pre-empting OPEC's decision, while the UAE's state oil firm ADNOC notified its lifters last week of bigger cuts.