Merlin, as the Leicester match is now sold out you've probably got little chance other than touts I'm afraid.
As for future matches, you can see the first day of sale dates on somewhere like
www.liverpoolfc.tv and if you're prepared to sit on the credit-card line and persevere as soon as it opens then you can normally get lucky. I did this for the Spurs game and have surprisingly managed it for B'burn away this morning even though there were supposedly only 7000 tickets and they've already been available to season ticket holders for a while. I was only on the phone for 15-20 minutes in each case.
Good luck..................