I'm assuming you're in England/ Wales?
If you're not on the market and haven't secured finance, you can express your intersest in the property and ask to be informed of any changes in status but you aren't in a proceedable position so its very unlikely any seller will take an offer seriously.
If you think yours will sell quickly you may be able to negotiate a price and timeframe that the sellers will stop marketing.
Tidy, seriously declutter your house and clean (its really worth considering shifting excess stuff out so its more of a lightly furnished blank canvas then cramped outgrown space). Go outside until your house is just out of sight and approach it as though its the first time. Can you park, is the path clear, is the front door welcoming i.e. tidy garden nice hanging basket or overflowing bins and broken bits you've been meaning to get to the dump. Do the window frames look clean, does the house look maintained or would a few hours make it look great?
In parallel contact several estate agents, get valuations and find out about fees and marketing schedule. There first impressions are important if you want the best price so think of it as a viewing but be honest.
Next go on moneysavingexpert and do the mortgage search thing where it doesn't effect your credit score and they indicate the sort of mortgage deals they think you'd be able to get.
Choose one, apply.
Choose best estate agent.
Sell house for lots of money, buy new house for cheeky low offer
(actually join the sellers support thread because you wont be the only one going through the pain)
Live happily ever after.