The 25-year-old, who has scored 23 goals in as many games in all competitions so far this season, has been heavily linked with a potential move to Stamford Bridge to link up with compatriot and former Shakhtar team-mate Willian.
The Brazilian has now said that the champions of France and Italy are also attempting to secure a deal but has admitted his dream is to one day play in the Premier League - though he says a January switch is unlikely.
"What I've seen, and what my manager has said, is that Chelsea, Juventus and PSG made offers. But Chelsea and Juventus are deeper into negotiations," he told Lance.
"They're three big clubs. Wherever I go, I'll be happy.
"It's my dream [to go to England]. I've spoken to many people who have the desire to play in the Premier League, because I think it's the best in the world, more contested, and I want to have this challenge in my career.
"I'm glad to have received that proposal from Chelsea, they're a great club in Europe, but my manager will deal with that.
"I think it'll be very difficult in January because it is in the middle of the championship. Shakhtar have said they won't let me leave in January, only at the end of the season."
Teixeira is eager for Chelsea to keep hold of Jose Mourinho as manager, despite their poor start to the season, as he would relish the chance to work with the former Real Madrid boss.
"He's the world's best coach. I think I would learn a lot from him," he said. "I hope he doesn't leave Chelsea now. I want to work with him and have great success at his side.
"He has this aggressive way because he always tries to be the best. I want to overcome this challenge."