The local elections are due to take place on 7 May 2009 with the European elections following a month later on 4 June 2009.
Local government minister John Healey has launched a consultation on whether the former should be pushed back to June.
The department said the move would make life easier for administrators as well as being more convenient for voters.
In 2004, the last time that the elections dates were changed to coincide, there was a 10.5% increase in turnout for the European elections. Previously there had been a 24.5% turnout in 1999.
Parish council elections may also be moved back to June.
“We want to see an efficient and secure electoral system which is as convenient and as straightforward for the voter as possible,” Mr Healey said.
“It is important to consider all the potential impacts of holding elections together. This is why our consultation document seeks views on whether or not it is better to combine elections.”