The Australian signed from Middlesbrough for £2.3m last August as a back-up to Jose Reina but has played just twice, in the Carling Cup defeat at home to Northampton and the Europa League against Utrecht in December.
He was loaned out to npower Championship side Derby and made his debut in Saturday's 4-1 defeat at Cardiff.
Newspaper reports suggested Jones has fallen out of favour with boss Kenny Dalglish and his backroom staff.
But the keeper wrote on Twitter: 'Completely untrue and really a poor attempt at a story.'
Jones spent almost 10 years at Middlesbrough but spent much of that time out on loan.
He made fewer than 60 league appearances for the Championship cluband his multi-million pound move to Anfield came as a surprise lastsummer.
Jones has also been capped three times for his country and was part of the squad that finished second in this year's Asian Cup.
Source: Daily Mail