Prop Willem Nel and winger Dougie Fife are the latest Edinburgh players to express their desire to see Alan Solomons remain as head coach.
They follow Sam Hidalgo-Clyne and Roddy Grant in hoping Edinburgh retain the 64-year-old South African, who is nearing the end of his two-year deal.
"It would be amazing for him to be here for as long as he can," said Nel.
"For us, it would be really great because of the systems he has brought in and what he brings out of us."
Solomons led his team to the European Challenge Cup final at the start of this month, where they lost 19-13 to Gloucester.
However, the players say the main goal is to qualify for the Champions Cup next season.
To do that, with a Pro12 top six place and automatic qualification looking unlikely, they must beat Leinster at Murrayfield on Saturday, and hope Connacht do not beat leaders Ospreys, to clinch seventh spot and a play-off against Gloucester.
If Edinburgh gained revenge against them, they would then have to beat the seventh-placed team in France's Top 14 to reach Europe's elite competition.
|Pro 12 remaining fixtures|
|Saturday, 16 May: Treviso v Scarlets, Cardiff Blues v Zebre, Connacht v Ospreys, Edinburgh v Leinster, Glasgow v Ulster, Munster v NG Dragons (all 15:00 BST)|
"We did really well in the Challenge Cup but just fell short," said Fife.
"Our main objective is to get in to that Champions Cup and play in the top flight in Europe. We've got the squad, I believe, that can play in that competition and do well."
That Edinburgh are still in the qualification mix is down not just to the players, but to Solomons, argues tighthead prop Nel.
"He put in some systems and there has to be a lot of credit for how the boys took them on," the South African told BBC Scotland.
"It didn't just happen for us, it took some time. Luckily, this year all the stuff just connected and we've had a good season."
And Fife added: "It always takes a while when a new coach comes in.
"We're a really tight team, we know what each other brings to the game.
"We know the game plan inside out. Before we go on the pitch we almost know exactly what is going to happen in each area of the pitch.
"Alan has brought a lot of confidence, as well. It's a good place here now.
"The boys respect him highly as a coach and as a man so hopefully he'll be around for the future of Edinburgh and he's going to bring the best out of us if he does stay."