Mr Crabb, who had stood to be the next Tory leader and Prime Minister, has been open about his deep faith in Jesus.
During his campaign for the leadership he referenced his faith and said he was a family man.
The Times newspaper claims to have seen an exchange of flirtatious WhatsApp messages with a young woman in the run-up to the EU referendum.
The married father of two was not contactable by Premier.
Mr Crabb told the woman he wanted to kiss her 'everywhere', The Times claims.
It said a source leaked the messages to a reporter because Mr Crabb was a hypocrite who told a hustings he should be trusted because of his values.
In an earlier exchange with the woman the politician is reported to have said the "public can't expect MPs to be angels".
Most are "risk takers... in the areas of money, sex, political opportunism," he said.
Mr Crabb, the Work and Pensions Secretary has said God's care for widows and orphans in the Bible is his "guiding star for social policy".