The Welsh Rugby Union (WRU) says it will honour existing contracts and also guarantee new contracts signed by players of national interest such as Edwards.
Jones is hoping Ospreys will not lose more players after Lake and Morgan’s departures.
“I’m pretty confident we will retain the players we want to, but ultimately I can’t think for a player,” said Jones.
“I can just look at it through my lens at how we are communicating to the players, the type of environment we want to set here and then the types of packages we are trying to put forward to the players.
“I’m confident we’ll make it difficult for players to move on with those things on the table.
“I am pretty confident there’ll be a very strong Ospreys squad here moving forward in the years to come.”
Jones’ comments about the Ospreys’ long-term future were made as he prepares his side to face Cardiff on New Year’s Day.
These derby fixtures come at a time when the Welsh Rugby Union (WRU) plans to cut a men’s professional side.
There are rumours that the Ospreys’ owners, Y11 Sports and Media, are in talks to buy WRU-owned Cardiff, who went into administration briefly in April before being taken over by Welsh rugby’s governing body.
The WRU announced in October it wants to reduce the number of teams to three, with licences to be granted in Cardiff, the west and east.
Negotiations have continued, but the WRU has announced that a decision on how a team will be cut will now not happen before the end of 2025.
It had seemed there would be a straight shootout between Scarlets and Ospreys for the west licence before this other proposal – of Y11 taking over Cardiff – emerged, one which would enable Welsh rugby bosses to get to their desired number of three.
The WRU and Y11 have both declined to comment on this possibility, fuelling fears of Ospreys supporters about their side’s future, while Cardiff fans have been vocal on social media against any such proposed takeover deal.
When asked whether he had been given any assurances for next season, Jones said: “I don’t deal in rumours, I can only deal in facts.
“I’ve got no facts that I’ve been spoken to about or heard internally that suggests there’ll be anything other than the four teams we’ve got at the moment.
“We are working off that at the moment. I’m sure the powers that be will come forward and update everybody.”