The question is will Gomez stay and fight for his place or decide the time has come to move on? He signed a new 5 yr contract (£75k p.w.) for the 2019/20 season (expiry 23/24) so there is no urgency to do anything, on the club's side.
He had this to say (I'm guessing tongue in cheek when assessing his competition ex. Konate) :
“That’s part and parcel of being at a top club, I think,” he told Liverpoolfc.com.
“That’s what this club deserves and that’s what we all thrive off: competition is good and it’s healthy. But we can all learn off one another, I think each of us is different and we’ve got top quality. “Obviously the likes of Rhys and Nat and Ben and so on, all top players, and it’ll be good this season. Now it’s just to learn from each other and keep pushing each other, day in and day out.”
On Konate specifically, Gomez continued: “Ibou’s top. He’s a great player and has adapted straight away to our style of play. Obviously it can be high-intensity sometimes but he’s got all the attributes to thrive I think.”
However it's clear to see the direction Klopp is moving in (from the Offal) :
Gomez looks to have improved his long-range passing during his time on the sidelines, with Klopp describing it as a “nice little asset.” “Having the centre-halves back, playing football, you can see Joey with new long balls from left to right to left, a nice little asset,” he told the club’s official website. “It’s good, we can switch the game quicker maybe.”
While Phillips and Williams can execute long-range passes at times, they are not able to do so with the consistency of Liverpool‘s established senior centre-backs.
That made the Reds more predictable in their absence, with opponents able to read their play more quickly and counter the threat of Sadio Mane and Mohamed Salah out wide. If Liverpool are able to “switch the game quicker,” as Klopp details, they can spot gaps in the opposition’s defence by springing accurate balls out to the likes of Mane, Salah, Andy Robertson and Trent Alexander-Arnold.
It is an asset that Ibrahima Konate possesses, too, with the Frenchman also blessed with the recovery pace that allows him, Gomez, Van Dijk and Matip to operate more comfortably in the high line Klopp desires.
I can't see him wanting to move at this time, not after the club's support, however if this season doesn't go well for him, playing time-wise, I'd expect he'd re-evaluate for next season.
