* Wheat on course to rise for third week on brisk demand

* Corn demand seen boosted by widening discount to wheat

* Soy, corn set for weekly losses as US harvest advances

(Adds quotes, updates prices)

By Nigel Hunt

LONDON, Oct 4 (Reuters) - U.S. wheat futures rose slightly on Friday, supported by brisk demand from Brazil and China, and were on track for a third straight week of gains.

Corn futures on the Chicago Board of Trade also edged up although remain on course for a weekly loss while soybean prices eased as the U.S. harvest continued to advance.

"Wheat and corn prices continue to diverge. Lower U.S. stock levels and strong demand from China and Brazil are providing impetus for wheat prices," Commerzbank said in a market note.

"In contrast, the stronger than expected upward revision of U.S. stock levels and the prospect of a record U.S. crop, which is currently being harvested, are having a negative impact on the price of corn."

December wheat futures on the Chicago Board of Trade Wc1 stood 0.3 percent higher at $6.91-1/2 a bushel at 1131 GMT. The front month is on track for a weekly gain of 1.2 percent.

"Wheat supplies are tight and the market has more upside potential," said Kaname Gokon, deputy general manager at Okato Shoji Co. in Tokyo. "The CBOT December contract could test $7.00 a bushel next week."

CBOT Dec corn Cc1 rose 0.2 percent to $4.40-1/4 a bushel. The front month is on track for a weekly loss of 3.0 percent.

Dealers said the divergence in prices between wheat and corn is likely to shift demand towards the cheaper grain.

"The potential glut of corn from the U.S., EU and Black Sea - when available - will compete with and shift demand away from wheat in feed diets," David Sheppard, managing director of UK merchant Gleadell said.

Commerzbank also expected a shift in demand.

"It is doubtful whether the price differential between wheat and corn will widen much further. For, given the already substantial price difference, corn is likely to be substituted for wheat to meet demand for animal feed," Commerzbank said.

Milling wheat futures in Paris were lower as the U.S. government impasse kept the euro around 2013 highs against the dollar with November BL2X3 off 0.50 euros or 0.3 percent at 194.50 euros a tonne.

CBOT soybeans also weakened with November Sc1 down 0.4 percent at $12.83-1/2. The contract is on track for a weekly loss of 0.4 percent.

Dealers said the market was weighed by talk that some yields in the early stages of the U.S. harvest may have been better than expected.

(Additional reporting by Naveen Thukral; Editing by Jason Neely)

((nigel.hunt@thomsonreuters.com)(44 020 7542 8421)(Reuters Messaging: nigel.hunt.thomsonreuters.com@reuters.net))

Keywords: MARKETS GRAINS/