The former Palermo man is edging closer to signing a new deal with the Trigoria-based outfit, as the clubs reach an agreement over undisclosed fee
The 22-year-old centre-back was granted permission by Felix Magath to travel to the Italian capital so he could sustain tests with Roma before signing a contract.
And, after heading to the Policlinico Gemelli on Friday, the former Palermo man affirmed that he is eager to embrace his new adventure.
"I am very happy to be at Roma. When [Walter] Sabatini called me it took me two seconds to decide," Kjaer is quoted as saying by Tuttomercatoweb.com.
"There is a great project here and I am very happy. I cannot wait to start this new adventure following a difficult year."
The Denmark international left Palermo for the Bundesliga last year, but he endured a less than perfect campaign, narrowly dodging relegation.
Neither club have confirmed the costs of the operation, but reports suggest Luis Enrique's side will pay around €10 million (£8.85m) for the transfer.