The Tamil Nadu batsman, who missed the 10th edition of the Indian Premier League, underwent a wrist surgery in London and has since been spending time recuperating and following the rehabilitation programme prescribed to him.
"I am in the process of recovering. Have a few more days to go. I want to be at my best fitness-wise," Vijay told PTI.
He is currently working in Chennai with Rajinikanth, a trainer at NCA, and hopes to start batting again in the coming days.
The stylish right-hander is likely to spend some time at the NCA in Bengaluru where his recovery would be assessed.
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With India slated to tour Sri Lanka for a series next month, Vijay is preparing himself for the same.
"I have had an operation. I am hoping all will be well and I should be alright by then.
"I am working on my fitness part. I can't rush my return as I have had a surgery. I will go by the doctors' advice."
Vijay, who has played 51 Tests so far, has also featured in 17 ODIs and nine T20 Internationals, is keen to be part of all the three formats.
"I know I have the game to play and do well in all three formats. For that fitness is an important aspect and I am working towards that," he said.
On the Virat Kohli-led team's performance in the tournament, he said, "Great to watch the way we are playing. It is our time to dominate."
T Due to the injury, Vijay said he got the opportunity to spend quality time with his family, which is a luxury for a modern day cricketer given the hectic match schedule and travelling.
"I am happy to have got the chance to be with my family, the children, especially. It was great to be at home more."
It was a fantastic experience to watch a game at the stadium, he said adding "I like to watch the big stars like (Cristiano) Ronaldo, Zlatan Ibrahimovic play.