Liverpool wanted to sell the 23-year-old in the summer and the midfielder was linked with clubs such as Juventus, Sevilla and Santos.
“When they told me, I said I will try to find a club, but that I would not go just anywhere,” Lucas said in the Daily Telegraph.
“[I said] I think I can be at a good club, since Liverpool is a good club and I had been here for three years.
“But I also said I would fight for my place, I will train, that I am a professional. It was not easy, but sometimes you have to be calm.
“A few offers came, but Liverpool did not accept them. I am glad that I stayed, because I am playing well, helping the team, and I am more important now than I was a few months ago.”