Maddison and Jones were part of Gareth Southgate's 33-man provisional squad, but both players have left England's training camp after being told they will not make the final cut.
Southgate must name his official 26-man squad by Friday's deadline, which is just after England play Finland at Wembley in their last warm-up ahead of the tournament.
The Euros start in Germany on June 14 and England are among the favourites as they chase a first major men's trophy for 58 years.
Maddison, 27, was introduced as a 61st-minute substitute in Monday's 3-0 friendly win against Bosnia and Herzegovina at St James' Park.
But Maddison, whose form tailed off for Tottenham following a strong start to the Premier League season, is among seven players who will not be on the plane to Germany.
Maddison, who went to the 2022 World Cup with England, has won seven caps but faced stiff competition in his position with the likes of Jude Bellingham, Phil Foden, Cole Palmer, Jack Grealish and Bukayo Saka.
"Devastated doesn't quite cut it. Trained well and worked hard all week but if I'm honest with myself, my form for Spurs when coming back from injury in the second half of the season probably wasn't at the levels I had set which gave Gareth a decision to make," he wrote on social media.
"I still thought there would be a space for me in a 26-man squad as I feel I bring something different and had been a mainstay in this whole qualifying campaign for Euro 2024 in Germany but the manager has made the decision and I have to respect that.
"I'll be back, I have no doubt. Wishing the boys all the luck in the world out in Germany, unbelievable group and lads that I literally call some of my best friends. I genuinely hope football comes home."
Along with Maddison and Jones, Liverpool's uncapped defender Jarell Quansah is also expected to miss out on a Euro place.
Meanwhile, Manchester United defender Luke Shaw has returned to training after a lengthy muscle injury, boosting his hopes of making the England squad.
The 28-year-old left-back, who scored against Italy in the 2021 final defeat, has not played since February and made just 15 appearances for United in all competitions last season.
Southgate's final squad is scheduled to be announced on Saturday, with England starting their Euro campaign against Serbia on June 16 before facing Denmark and Slovenia in their other Group C fixtures.