But, Romney, the party's 2012 election standard-bearer, stopped short of an official endorsement as he urged voters to deny the nomination to front-runner Donald Trump.
In a Facebook post, Romney said a vote for Cruz in Utah's caucus on Tuesday was the best way to prevent Trump from locking down the nomination, which would give opponents a chance to select another candidate at the party's July convention.
"The only way we can reach an open convention is for Senator Cruz to be successful in as many of the remaining nominating election as possible," Romney wrote.
Romney did not offer any praise for Cruz, who emerged as a favorite of the party's most ardent conservatives after clashing with party leaders in Washington. Romney did not say whether or not he would campaign with Cruz.
Trump responded quickly.
"Mitt Romney is a mixed up man who doesn't have a clue. No wonder he lost!" he wrote on Twitter.
The Cruz campaign did not immediately respond to the news.
Romney has emerged as one of the most prominent critics of Trump, the businessman and former reality TV personality who has emerged as a surprise front-runner in the battle to secure the Republican nomination for the Nov. 8 election. Romney, who lost to Democratic President Barack Obama in 2012, called Trump a "fraud" and a dangerous demagogue who would lose to Hillary Clinton, the Democratic Party front-runner, in November.
"Today, there is a contest between Trumpism and Republicanism, Romney wrote, adding that Trump has encouraged racism, misogyny and violence.
"I am repulsed by each and every one of these," he wrote.
Trump has continued to notch victories in the state-by-state nominating process as Republicans have failed to unite behind Cruz or Ohio Governor John Kasich, the only other candidate left in the race.
At this point, those who oppose Trump say their best bet at this point is to prevent him from securing the 1,237 delegates he needs before the convention in Cleveland.
Cruz is unlikely to win the nomination outright as he would need to win 81 per cent of the remaining delegates to reach a majority, according to the Cook Political Report.
It is impossible for Kasich to reach 1,237 delegates, according to the nonpartisan election tracker.
Romney said Kasich has a "solid record" as a governor and he would have voted for him in Ohio last Tuesday.
Other Republican leaders have struggled to choose between Trump and Cruz. Cruz has won the endorsement of only two of his fellow Republican senators, for example, while only one has endorsed Trump.
"If it was truly an anyone-but-Trump mindset that had taken hold, we would've seen a much more aggressive move to Cruz and we haven't," a senior Senate Republican aide told Reuters on condition of anonymity. "Most members truly don't know which one is worse."
