Collins said the duchess pitched paid family leave, an issue currently gripping the US.
"Much to my surprise, she called me on my private line and she introduced herself as the Duchess of Sussex, which is kind of ironic," Collins added.
"I was happy to talk with her, but I'm more interested in what the people of Maine are telling me about it."
Last month, Markle, who lives in California with Prince Harry and their two children, posted a letter to Congress on the website PaidLeaveforAll.org calling for paid family leave in the US.
"I'm not an elected official, and I'm not a politician. I am, like many, an engaged citizen and a parent. And because you and your congressional colleagues have a role in shaping family outcomes for generations to come, that's why I'm writing to you at this deeply important time—as a mom—to advocate for paid leave," Markle wrote.
The development came after royal experts claimed she is attempting to forge a political career. Markle this week sent workers from organisation Paid Leave US$25 (around $30) cash for coffee.
Charity comms boss Neil Sroka tweeted: "The Duchess of Sussex (aka Meghan Markle) bought everyone at Paid Leave US a few cups of coffee while we're working overtime to save paid leave.
"Unbelievably classy … and necessary.
"Truly honoured to know she has our backs in the fight to win paid leave for all."
Meghan revealed earlier this month that she and Harry have been "overwhelmed" by the birth of second child Lilibet as she pushed for paid leave for parents.
In a letter to two Democratic politicians in Washington DC, she urged the government to ensure new parents can have time off work with their babies.
America has no system for paid parental leave, although President Joe Biden has vowed to introduce it.
In her letter, addressed to Democrats Chuck Schumer and Nancy Pelosi, Meghan discussed being lucky enough to afford time off with Harry after the birth of Lili in June.
She said: "Like any parents, we were overjoyed. Like many parents, we were overwhelmed.
"Like fewer parents, we weren't confronted with the harsh reality of either spending those first few critical months with our baby or going back to work.
"We knew we could take her home, and in that vital (and sacred) stage, devote any and everything to our kids and to our family.
"We knew that by doing so we wouldn't have to make impossible choices about childcare, work, and medical care that so many have to make every single day.
"No family should be faced with these decisions."