It’s understood the English Premier League club tabled a £5 million offer for 19-year-old Patterson at the end of last week which was immediately rejected by the Scottish champions.
It remains to be seen whether Everton will return with an improved bid before the transfer window closes in nine days’ time.
Asked if an initial offer had been received, Gerrard replied: "Not to my knowledge. I'm sure the right person will tell me if that's the case and if there's truth in it.
"I hear a lot of noise and a lot of rumours. A lot of talk about a lot of our players. The only people I listen to in this situation are (sporting director) Ross Wilson and the board. If any bids land and they're respectable then we'll discuss them."
Patterson, who is regarded as one of the brightest young talents in Scottish football, signed a new contract with Rangers in January this year which runs until the summer of 2024.
He has made just 17 first team appearances so far but has emerged as a genuine contender for the right-back role currently held down by club captain James Tavernier.
Patterson’s outstanding form in the second half of last season, when he deputised for the injured Tavernier, earned him a call-up to the Scotland squad for this summer’s Euro 2020 finals where he earned his second full cap as a late substitute in the final group game against Croatia at Hampden.