MONEY MARKETS-Dollar costs for European borrowers hover near high

* Three month eurodollar basis swaps hover near May peaks

* Borrowing costs to stay high for European names

* Korea basis swaps under upward pressure on tensions

HONG KONG, Dec 20 (Reuters) - Eurodollar basis swaps on Monday stayed within sight of their highest levels since the Greek debt crisis broke out in May as funding conditions remained grim for the continent’s weaker banks.

On Monday, dollar forwards upto one month maturities were trading at a small premium -- indicating borrowers were shelling out more to get access to funds and traders said this premium might rise further until the year end.

Friday’s multi-notch downgrade of Ireland’s credit rating served a grim reminder to the ongoing woes of Europe’s debt crisis.

“We are going to see this dollar shortage for European names get worse before it gets better and currently the peripheral names are getting pinched due to this,” said a trader at a bank in Singapore.

Three month eurodollar basis swaps , which measures the cost of swapping euros for dollars, had widened to minus 67 basis points (bps) last Thursday -- its highest level since May -- from 51 bps at the start of December revealing the worsening situation. On Monday, they pulled back by 2 basis points to minus 6 5 bps, meaning European borrowers needing access to dollars will have to pay an extra 65 bps over and above paying LIBOR.

One trader at a European Bank in Singapore said there is also a noticeable pick up in dollar demand from some offshore branches of Chinese banks who were willing to pay a premium over LIBOR, which kept the upward pressure on funding costs intact.

In funding markets, three month dollars in Singapore fixed a shade lower at 0.30484 percent but was well within reach of its highest levels so far this month.

In Korea, basis swaps remained under upward pressure in thin year-end markets due to heightened tensions on the peninsula after local media reported that Seoul planned to go ahead with live-firing drills from a disputed island. [ID:nL3E6NK01M].

One-year basis swaps, which measures the cost for swapping won for dollars, has widened to near 180 bps from around 100 bps in September and traders said this rate could easily rise to 250 bps, an early 2009 peak, if tensions escalate further.

Editing by Kazunori Takada