This is the first reported interest in Tate since free agency got underway a few weeks ago.
Even though the Chiefs signed Jeremy Maclin at the start of free agency, they could still use some help at receiver.
Tate, 27, is a former third-round pick of the Patriots back in 2009. He lasted just two years in New England before he was waived and later claimed by the Bengals.
In 2014, Tate appeared in all 16 games for the Bengals and caught 17 passes for 193 yards receiving and a touchdown. He also returned kicks and punts for Cincinnati.