The Toffees have made four signings during the ongoing transfer window following the arrival of Rafael Benitez, but are keen to strengthen their squad further.
Everton are keen to bolster their options at right-back and have been linked with the likes of Aurelio Buta and Denzel Dumfries.
Rangers full-back Patterson has become the latest player to be linked with a move to Goodison Park, with Everton eyeing him as a potential recruit.
The Merseyside-based club stepped up their interest in the 19-year-old by approaching the Scottish Premiership champions with an offer on Friday.
Everton’s offer for the Scotland international is claimed to be £5m and it remains to be seen if Steven Gerrard’s side will accept it.
Rangers have spoken about their plans to run an effective player trading policy, but have not made a major sale so far this summer.
It remains to be seen if the Light Blues will cash in on Patterson in an attempt to raise funds or decide to hold on to one of their most promising youngsters.