But he was quick to end any such speculation when he used social media today (Saturday July 9) to rule himself out.
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He sent messages out on Twitter to make the point, stating: “After careful consideration and discussing with colleagues and family, I have taken the decision not to enter the contest for leadership of the Conservative Party.
"It has not been an easy choice to make, but my focus is on my current job and keeping this great country safe.
"I wish the very best of luck to all candidates and hope we swiftly return to focusing on the issues that we are all elected to address.”
Johnson resigned on Thursday when his position became untenable after a series of mass resignations in the government, following a string of scandals.
Mr Wallace is regarded as being loyal to Johnson and ran his successful leadership campaign in 2019.
Before his political career he served in the Scots Guards and saw service in Germany, Cyprus, Belize, and Northern Ireland during the 1990s, being promoted to Lieutenant.
He was first elected as MP in 2005 when he took the Lancaster and Wyre seat, which had previously been a Labour constituency.
The constituency was abolished for the 2010 general election, and Mr Wallace was elected for the new seat of Wyre and Preston North, to which he was re-elected in the 2015, 2017, and 2019 general elections with a sizeable majorities.
The Conservative leadership contest got under way yesterday when former Chancellor Rishi Sunak announced his campaign.
Mr Sunak is the most high profile candidate so far to put his name forward.
Other candidates to come forward at this stage are Suella Braverman, Attorney General for England and Wales, and Kemi Badenoch, Minister for Women and Equalities.
Mr Johnson’s premiership lasted just three years and was beset by the Covid pandemic and a series of crises, including the so-called Partygate probe and revelations of grope allegations regarding former deputy chief whip Chris Pincher,