A grand jury probe, which involves a prosecutor pursuing allegations with an eye toward possible indictment, typically represents a legal escalation, though it does not always lead to prosecution.
Melgen has provided Menendez with plane flights and hospitality at his Dominican vacation home, people acquainted with their relationship say.
Last month, people with knowledge of the case said FBI agents were conducting interviews in the Dominican Republic and the United States concerning allegations against Menendez, including the role he played in advocating for the enforcement of the port security contract.
Menendez declined Thursday to say whether he knew anything about the investigation, but he said any probe would find no wrongdoing.
"I welcome any review, because I believe, at the end of the day, that my actions have been appropriate," he said. "And just as everything that gave rise to this was a smear campaign based on slanders that drove the original story, I believe that when any review reviews the facts, they will determine that I have acted appropriately at all times."
As part of the grand jury inquiry, the three people said, federal agents have questioned witnesses about the interactions between Menendez and Melgen, who contributed $700,000 last year to Menendez and other Senate Democrats.
The grand jury has also issued subpoenas for Melgen's business and financial records, according to two people briefed on the probe who, like the others, spoke on the condition of anonymity to describe an ongoing investigation.
Federal agents have not contacted Menendez, according to a person familiar with the case.
The senator, who chairs the Senate Foreign Relations Committee, acknowledged in January that he had previously failed to disclose two free trips he took on Melgen's private plane to vacation with him in the Dominican Republic in 2010.
Menendez said he wrote Melgen a personal check this winter for $58,500 to reimburse him for the plane rides. The Senate ethics committee is investigating why Menendez did not disclose the flights sooner.
Menendez said Thursday that his failure to disclose the flights was a mistake resulting from confusion about his frequent travel during 2010, when he was heading the Democrats' Senate campaign committee.
"In the midst of all of that travel, flights that should have been filed in a different way weren't," he said.
He said he could have likely received an exemption from the Senate ethics committee based on his long friendship with Melgen. "But I said, 'You know, it's past, and the right thing at the moment is to pay for it,' " he said. "When I learned of the mistake, I did what was right and took care of it."
Melgen attorney Kirk Ogrosky said the eye doctor was proud of his relationship with the senator and had no worries about any federal investigation.
"Dr. Melgen has been a friend and supporter of Sen. Menendez for over 20 years," Ogrosky said. "We are confident that any inquiry will determine that Dr. Melgen acted appropriately at all times."
A spokesman for the FBI's Miami office declined to comment.
The investigation, which is still in its early stages, began with two disparate issues, according to people familiar with the matter.
First, auditors had, for some time, been reviewing allegations that Melgen was fraudulently overbilling Medicare for treating his patients. Melgen's attorney has said that the doctor's billing was completely appropriate.
Then, in the fall, the FBI began looking into an anonymous tipster's allegations that Melgen had arranged prostitutes for Menendez in the Dominican Republic. Such an arrangement could constitute providing a favor or gift under the bribery statute that investigators have been reviewing.
Lawyers for Menendez and Melgen have repeatedly said the allegations involving prostitutes, which were also made by a conservative website, the Daily Caller, are false and absurd. Menendez has said that the allegations, which first surfaced during his reelection campaign last year, are part of a Republican smear campaign.
So far, FBI agents investigating leads in the Dominican Republic have found no evidence that Menendez patronized prostitutes there, according to two people familiar with the probe. Last week, a Dominican escort said in sworn court statements that she was paid to fabricate claims that she had sex with Menendez for money.
Stan Brand, a veteran defense lawyer, said establishing evidence of a crime in a scenario like that being examined by the Miami grand jury would be a "real tough row to hoe" for investigators and prosecutors. Federal bribery laws require proof that a politician received something of value with the express purpose and understanding that it was to influence his or her official action.
"You must show an absolutely direct nexus between the thing of value and the intent and the official act," Brand said.