Meehan's comments to the Inquirer are his most extensive since The New York Times reported Saturday
that the Pennsylvania Republican had used thousands of dollars in taxpayer money to settle a sexual misconduct complaint against him by a former aide.
In the Inquirer interview, Meehan also said he still plans to seek re-election.
Meehan told the Inquirer he had "developed an affection" for his aide "in a way in which I was struggling to make sure that I would never put that into our professional relationship."
He expressed his feelings to the woman and later that night wrote her a letter by hand, according to the Inquirer.
Meehan, according to the Inquirer, said he never wanted a romantic relationship with the former staffer and that he remained loyal to his wife.
He told the Inquirer that he had told the woman he was "a happily married man and I was not interested in a relationship, particularly not any sexual relationship, but we were soul mates. I think that the idea of soul mate is that sort of person" with whom you can "go through remarkable experiences together."
Alexis Ronickher, the attorney for Meehan's accuser, told CNN that his comments were a "gross violation of the agreement" between her client and him.
"At this time, my client sees this as a continued breach of the confidentiality agreement," Ronickher told CNN. "She continues to prize her privacy and is not going to breach. What she will do is cooperate with the Ethics Committee investigation and provide any and all information she can. She's right now reviewing what legal actions and remedies are available to her."
The House Ethics Committee announced Monday that it had opened an investigation into Meehan in response to The New York Times report.
The chairman and ranking member of the House Ethics Committee said Monday that the panel had begun looking into allegations that Meehan "may have engaged in sexual harassment and misused official resources, namely his Member's Representational Allowance." They also noted that Meehan himself had written to the committee to ask that it review the allegations.
The former aide accused Meehan of making unwanted romantic advances toward her and growing hostile when she didn't reciprocate, according to the Times, which cited people familiar with her time in the office.
The former aide initiated a complaint with Congress' Office of Compliance, began working from home and ultimately left her job, the Times reported. She later reached a confidential settlement paid from Meehan's congressional office fund.
Meehan told the Inquirer on Tuesday that he would repay the public funds used to settle the case if the House Ethics Committee's investigation finds that he harassed the woman. However, according to the Inquirer, Meehan described the payment as "severance" rather than a "settlement."
Meehan had been a member of the House ethics panel but was removed by House Speaker Paul Ryan on Saturday. Ryan also told Meehan he must repay whatever taxpayer funds were used to settle the case.
The allegations against Meehan surfaced the same week that a bipartisan group of House lawmakers unveiled a long-awaited plan aimed at tackling the way workplace complaints -- including sexual harassment -- are handled on Capitol Hill. Part of that legislation would hold lawmakers personally liable for settlements.