* Market sees more than 50% chance SNB will cut rates by Sept
* Interest rate cuts by ECB could force SNB to act
* Swiss franc has reached highest level vs euro in two years
* Swiss banks consider how to react to any interest rate cuts
By John Revill
ZURICH, July 24 (Reuters) - Financial markets see an increasing chance the Swiss National Bank will cut its deeply negative interest rates after the safe-haven franc hit two-year highs ahead of a European Central Bank meeting expected to signal easier policy in the euro zone.
On Wednesday, money markets were pricing in 54% chance the SNB will cut its benchmark rate of -0.75% -- already one of the lowest in the world -- by 25 basis points by September.
The probability increases to 72% for the SNB to cut its interest rate by December, a move designed to head off inflows into franc and limit the damage any further rise would inflict on the export-reliant Swiss economy.
On Tuesday, the probability for a cut by September was seen at 35% and 62% by December.
The main driver for a cut is the increasingly expansive mood at the ECB, with money markets pricing in around a 40% chance of a 10 basis point cut in its own deposit rate -- currently -0.40% -- when policymakers meet on Thursday.
The Swiss franc also breached the 1.10 barrier versus the euro on Tuesday to hit its highest level since July 2017.
"If there is a cut by the ECB there is a good chance that the SNB trails the ECB and cuts rates as well," said UBS economist Alessandro Bee. "If the ECB cuts rates this week this would certainly lead to more appreciation pressure on the Swiss franc."
Pressure would mount on SNB Chairman Thomas Jordan if the ECB's move -- designed to support inflation and growth in the euro zone economy -- is seen as part of a strong and sustained easing programme.
"If the ECB only cuts once and doesn't do much more, the SNB is not forced to move," said Frank Haeusler, chief strategist at Vontobel Asset Management. "But if the ECB announces another interest rate reduction or further bond purchases, the SNB will have to act."
The SNB would prefer currency interventions, said Thomas Stucki, chief investment officer at St Galler Kantonalbank and former head of asset management at the SNB.
"We have seen already that people are beginning to hoard money in Switzerland, and if the SNB cut rates further this would increase as the banks passed on the negative interest rates to their customers.
"If the ECB cuts its deposit rate by 10 basis points to minus 0.5% the SNB is not forced to reduce rates. But if the ECB cuts its deposit rate by 25 basis points, then the SNB ... will have no choice."
The SNB declined to comment. Chairman Jordan said last month he still has room to manoeuvre and could introduce even more expansionary monetary policy.
Switzerland's banks are also weighing how to react to further negative interest rates, which cost them nearly 600 million francs this year. The SNB steers its policy rate through a negative deposit rate which is effectively a charge paid by banks to park cash securely at the central bank.
"If there are any other conditions or particular feature of any new monetary policy ... then we will look at any alternatives to protect our margins," UBS Chief Executive Sergio Ermotti said on Tuesday. (Reporting by John Revill, Angelika Gruber and Oliver Hirt; Editing by Catherine Evans)