The 44-year-old sports star and his fiance are facing difficulties in their relationship but he claims they have not given up on their three year romance.
He tweeted: ''Some of the reports re EH & me r absolute rubbish. Yes we're sorting through some (private) issues. But we're not throwing the towel in yet (sic)''
Meanwhile, Liz - who has been engaged to the retired cricketer since September 2011 when she was spotted wearing a large sapphire ring - is trying to deal with her ''raw'' feelings.
She told her 400,000 Twitter followers: ''Apologies to loyal followers for Twitter silence on recent events. Too raw & personal to share right now. (sic)''
It is believed the 'Gossip Girl' star recently discovered her fiancé - who splits his time between England and his native Australia - has been getting close to his ex-wife Simone Callahan who he was married to for 10 years.
A source previously said: ''Liz found out he had been over at Simone's house a lot. She seemed to get the idea that something more than friendship was going on.''
Shane ended his marriage to Simone - the mother of his three children, Brooke, 16, Jackson, 14, and 11-year-old Summer - in 2010 and quickly began dating mother-of-one Liz, who has an 11-year-old son, Damian.
Liz was previously married to Arun Nayar in 2007 and three months after her divorce was granted in 2011 it was reported that her and Shane were engaged.