NBC, which airs the morning talk show, has reportedly reached out to the CNN star to replace the veteran host amidst speculation about the talk show's declining ratings and criticism directed at Lauer following the departure of his former co-host Ann Curry.
Network officials have made an offer to Anderson, 45, but when they approached Matt for his blessing, the TV star reportedly expressed his unhappiness to the TV bosses.
Matt, 55, supposedly reached out to his potential successor informing him of his disapproval, but the call came as a surprise to Anderson, who assumed NBC chiefs had sought the presenter's blessing before approaching him.
Anderson currently hosts two shows, including 'Anderson Cooper 360°' for CNN and a syndicated talk show, 'Anderson Live', which is set to be cancelled at the end of its current series. It's thought his contract with CNN would allow him to host programmes elsewhere.
Matt - who is reportedly on a $25 million salary - has been hosting 'Today' since 1996.
The show has fallen behind ABC's 'Good Morning America' in the ratings following 16 years at the top of the heap and the decline is being blamed on the presenter.