According to The Mirror, the Magpies are willing to double the two central defenders' salaries in a bid to lure them to St James Park.
Howe is a big fan of both Mee and his defensive partner Tarkowski, and with both players out of contract at Turf Moor next summer, there is optimism they can convince Burnley to cash in on the pair at the turn of the year.
It's understood the pair are currently on £50,000-a-week and Newcastle are willing to offer them a big pay increase to lure them to the north east.
Another reported target in defence is Lille's Sven Botman, who is valued at around £40million by the Ligue 1 club.
Botman graduated from Ajax's famed academy and left the Amsterdam giants to sign for the Ligue 1 club last summer, in a deal worth around £7.8million.
The 21-year-old Dutchman was strongly linked with a move to Liverpool last season following his impressive debut campaign at Lille.
The new billionaire owners are also planning to bring in a striker in the January window and a swoop for Stoke City star Tyrece Campbell is also in the pipeline, The Sun report.
It is said Howe is ready to offer £20m to get the 21-year-old to Tyneside once the transfer window opens.
Campbell started last season brightly with six goals and seven assists in 16 appearanes, before a severe knee injury hampered his progress.
But he is beginning to pick up form this term following his return to fitness, having struck two goals in nine Championship games so far.
Howe will undoubtedly have to sign players in January in order to maintain a survival bid for his side.
The Toon Army finally got their first win of the season last time out as they sunk Burnley at St James' Park.