Last month, Mr Musk, who owns 20 per cent of Tesla stock worth $9 billion, reached a settlement with the US Securities and Exchange Commission (SEC) under which he steps down as chairman of the electric auto maker and pay a $20m fine to settle fraud charges over his claims about taking the company private.
The Journal reported that Federal Bureau of Investigation agents have issued subpoenas to some former Tesla employees.
"We have not received a subpoena, a request for testimony or any other formal process, and there have been no additional document requests about this from the Department of Justice for months", she said in a statement.
The FBI did not immediately return a call seeking comment.
Tesla first disclosed in September that the DoJ was investigating Musk's tweets about having "funding secured" for a deal to take Tesla private, saying the agency had asked for documents about such statements.
Agents are probing whether Tesla "misstated information about production" and misled investors starting in 2017 about its ability to meet manufacturing goals, the Journal report says. Touching on this point late a year ago, Musk said that the "Model Y will, in fact, be using substantial carry over from Model 3 in order to bring it to market faster" and that it will "have relatively low technical and production risk as a result".
Musk pledged in the summer of 2017 that the company would be churning out 5,000 cars per week by the end of past year.
Such statements were fraudulent, according to the lawsuit, given that the automated assembly lines to build the vehicle in such volume were behind schedule.
Tesla finally hit its Model 3 production target in June of this year, about six months late.
Musk and Tesla only recently settled with the U.S. Securities and Exchange Commission over Musk's August 7 tweets. In the settlement, Musk and Tesla agreed to each pay a fine of $US20 ($28) million, with Musk also forced to step down as Tesla's chairman for at least three years.
Shares of Tesla rose 4.5 to $329, extending their rally following bullish results on Wednesday.