Vardy, 29, has not scored for the champions since 10 September - a run of 14 games - but netted in England's 2-2 friendly draw with Spain last week.
His form is in stark contrast to a year ago, when he scored for a record 11th Premier League game in a row.
"He has restarted and is very close to scoring," said Ranieri.
"He has started to also score in training, and that is good news because also, in the training, he didn't score so well."
Vardy has scored twice in the league this season compared with 13 at the same stage in 2015-16. He finished last season with 28 goals in 48 appearances for club and country.
Since his last club goal, the Foxes have slipped to 14th in the table with just two wins in nine matches.
Ranieri believes Vardy and team-mate Riyad Mahrez no longer boast the "surprise" factor that worked in their favour last season.
The Italian said: "That is the big problem. Jamie is always normal, the same last season. You don't see him nervous or frustrated.
"But sooner or later Vardy will come back. I speak every day with him. He is very calm, very concentrated in his job, to work for the team."
Leicester, who have qualified from their Champions League group with a game to spare, host Middlesbrough in the Premier League on Saturday (15:00 GMT).
Leicester boss Claudio Ranieri has backed Jamie Vardy to end his goal drought, but revealed the striker has even struggled to score in training.