The Norwegian is a free agent having left Premier League club West Ham in the summer and Inter are looking for back-up to Antonio Cassano with Argentinian forward Diego Milito ruled out for the rest of the season with knee ligament damage.
Having located the player at his hotel in central Milan, the Gazzetta dello Sport have joined Sky Sport Italia in reporting that the 33-year-old has been training with the club and could sign a 300,000 euro deal subject to passing a medical.
Carew told Gazzetta reporters: "I'm ready. I feel good and I've worked with the team over the last two weeks.
"I've travelled around and been to the cinema a few times but now I'm ready to give my all for Inter. I wasn't expecting the call - life is full of surprises."
Carew, who scored 24 goals in 91 appearances for Norway, has prior experience of Italian football having enjoyed a loan spell at Roma in the 2003-04 season.
Inter president Massimo Moratti told Sky Sport Italia: "Carew will have a couple of weeks try-out and then we'll decide if we take him.
"He has had an important career. We must consider whether there is also the physical shape, the will and all that is needed to be useful in the season finale".
John Carew's agent, Per Arne Flod, told calciomercato.it: "John is physically fine. He has no injuries and the first tests did not reveal any problems.
"Clearly being stopped for eight months, he may have a lack of match rhythm. But he is ready to give his best and, if he is given the opportunity, he will demonstrate his value."