Wells remained in St. Louis on Sunday. He has been put on anticoagulants to prevent a possible blood clot from forming.
"Right now, Kip is in the process of determining if he is going to get a second opinion of what the diagnosis is, and the different options that are available," said Pirates general manager Dave Littlefield.
Littlefield also said, "the action of the throwing [motion] has been identified as what had caused the blockage."
Wells is expected to decide if he will seek a second opinion within 24 hours. Should Wells accept Thompson's diagnosis, he likely would undergo surgery later this week.
Thompson performed similar corrective surgeries on Arizona Diamondbacks outfielder Luis Terrero in 2003 and Colorado Rockies right-hander Aaron Cook in 2004. In both cases, the player's top rib on the right side was removed and a vein was rerouted to the wrist.
Although the condition is serious, Littlefield said Wells' life was never in danger.
"It was not an emergency situation," said Littlefield. "There is always a concern in regards to clots, aneurysms, things like that. Evidently we moved on it very quickly."
Wells last threw off of the mound on Wednesday. When he could not properly grip a ball the next day, he was examined by the team's medical and training staffs in Bradenton. It was discovered that there was a difference between the pulse rates of Wells' arms.
"That gave them an indication that it was more serious than the 'dead arm' that we talk about in baseball terms," said Littlefield. "I compliment the doctors from a standpoint of detecting this."
Wells then was sent to Manatee Memorial hospital for additional testing. When a surgeon there expressed concern over the possibility that Wells might have a blood clot, the team advised Wells to travel to St. Louis to visit Thompson, who is considered the foremost expert in the field.
"We obviously wanted to get him to an expert in that area," said Littlefield. "Once [Thompson] examined him and had all of the information, he did the angiogram to get kind of the gold standard of evaluations."
Littlefield said it is too early to speculate on whether Wells' career, or at the very least his season, is in jeopardy.
"Right now, I don't think we're at that point," said Littlefield. "We'll have to wait and see what the second opinion is, if that's where he goes, and then we'll prepare for it once we get that information.
"We're always looking at the 'what if' scenarios that take place in any position, so you're always prepared for those things. At the same time, until the experts give us a confirmation, I am not in a position to outthink the experts."
Should Wells decide to accept Thompson's diagnosis and undergo surgery, it is unlikely that he'll be able to recover in time to pitch again this season. Terrero was out for five months after his surgery. Cook missed eight months before beginning a Minor League rehab assignment.
Littlefield spoke to Wells on Saturday night and said the pitcher was "concerned and disappointed."
"Players work hard in the offseason and don't want to have setbacks," said Littlefield. "Just to go through this procedure, [Wells knows] that regardless of where it goes it's going to set him back a little bit. But I think he's anxious to get it resolved and see where we go."
Wells' latest physical difficulty is not believed to be related to the elbow and circulation problems that forced him to miss action in 2004. Wells underwent carpal tunnel release surgery in October 2004 to eliminate the numbness he had been experiencing in the middle finger of his pitching hand.
Wells, who went 8-18 with a 5.09 ERA in 33 starts in 2005, signed a one-year, $4.15 million deal in January. He'll be eligible for free agency for the first time after this season.