The pair have been selected for Wednesday night’s friendly against Italy in Switzerland.
They joined Spurs team-mates Jermain Defoe and Kyle Walker for their first training session with Roy Hodgson on Monday.
“It’s fantastic news and I’m really happy, it’s just nice to know that all the hard work has been recognised,” said Jake, who made 38 appearances in all competitions in his breakthrough season last term.
“It’s the pinnacle really and it would be great now to be involved in some way - it would be something special to get a first cap.”
Steven, who has just returned to pre-season after representing Team GB in the Olympics, added: “It’s an amazing feeling, to get a first senior call-up. It’s what I’ve dreamed of since I was a kid. I didn’t think much could top the Olympics, but this is great.
“It would be a dream to get that first cap and it doesn’t come much bigger than Italy! It would be a fantastic moment.”