Republic of Ireland international Connolly has made just one top-flight start all season and been heavily linked with a switch to Championship club Middlesbrough.
The Galwegian was left out of Stephen Kenny's most recent Ireland squads, with former Bohemians' youngster Evan Ferguson seemingly now ahead of him in the Brighton pecking order.
The 21-year-old was left out of Albion’s squad for the 2-0 Boxing Day win over Brentford and the subsequent 1-1 draw at Chelsea.
Asked if a short-term move to the second tier would be beneficial for all parties, Potter replied: “I think it is.
“I’ve nothing to confirm yet but I think that’s the intention.
“Aaron is at the stage where he needs to play football and, if we can find the right fit, then that will work for him and for us.
“There comes a point when you need to play, you need to let football do the talking.”
In terms of incomings, Brighton continue to be linked with Poland international Kacper Kozlowski.
The Seagulls have a track record of recruiting young talent from abroad and Potter revealed his admiration of 18-year-old Pogon Szczecin midfielder Kozlowski.
“There’s nothing to confirm but I think he’s the type of player we’d be interested in,” said Potter.
“We’re always looking for players that can help us in the now but also in the future as well and you’ve got to find that right balance.
“The club have done it well so far and we’ll continue to do that.”
Potter also insisted the Africa Cup of Nations is an “important tournament” and says Yves Bissouma has the club’s blessing to play in it.
Mali midfielder Bissouma is among a host of Premier League stars set to be unavailable for domestic action early in the new year after being recalled by his country following a three-year absence.
Former England striker Ian Wright said on Thursday that the AFCON, which runs from January 9 to February 6, is being “disrespected” by some negative media coverage.
Despite being poised to lose the influential Bissouma following Sunday’s trip to Everton, Potter recognises the importance of players’ international careers.
“He’s due to go, so he goes with, of course, our blessing and I hope he does well and good luck to them (Mali),” said Potter, who worked in Africa earlier in his career during a spell as technical director for the Ghana women’s team.
“Playing for your country is a fantastic thing and we support our players in that. It is what it is and you just have to adapt, we know that.
“We wish him well because it’s an important tournament, it’s an important occasion for him and his family.”
Bissouma, who was born in Ivory Coast, won the last of his 18 Mali caps in October 2018 before reportedly falling out with the coach.
Brighton head to Goodison Park boosted by taking four points from six during the past week.
Leandro Trossard, who opened the scoring against Brentford before missing the trip to Stamford Bridge due to a tight hamstring, could return to action on Merseyside.
“He’s trained today, so that’s good news for us, we’ll see how he reacts to that,” Potter said of the Belgium forward.
“There was no injury, it was more fatigue and precaution based on the tight turnaround of the games. We’re hopeful he will be available.”