Should I save for deposit or try to pay off existing mortgage?

We have a 2 bedroom house with approx Euro 165,000 to pay off. The mortgage was for 30 years and we have 20 years to go. We are on a vairiable rate and in negative equity of approx Euro 80,000 - 90,000.
Ideally we would like to sell and move to a bigger house. I would like to do this in the next 2 -5 years.
I have Euro 6,000 in savings. I would like advise on whether I should put it into the mortgage as a lump sum. Is there any benefit to this? Or should I hold onto this money and try and grow it for a deposit on a new house?
It may not be possible for us to move as our income has greatly reduced since we bought the last time.

putting the 6K onto the mortgage won't make much of a difference for your monthly repayments I'd say; but the worst is that you won't have any savings left!
On pure mathematical basis it would be the best return for your money (that is, whatever variable rate you pay) but again....

Within your timescale of 2-5 years many things can happen so I'd just keep on saving as much as you can/want and then have a look again at the NE situation etc.
Many (well, some at least) banks also do deals where you can "top-up" the mortgage to buy a bigger house. No point guessing though what the situation will be in 2-5 years.

Save it, definitely.