The midfielder returned to the Three Lions squad this week after missing out through injury in November.
He has broken into Roy Hodgson's side this season, winning three caps, after impressing despite Villa's battle against relegation.
England face Lithuania on March 27 in a Euro 2016 qualifier before going to Italy for a friendly and Sherwood believes Delph can be at the heart of their challenge next year.
He said: "I've told Fabian he could be on the verge of something big
There's competition there but he could be a big part of it.
"Roy loves him
I spoke to Roy about him
When I was coming here I spoke to Roy about a few things.
"Roy will stumble across a team that will win the Euros
He will, I tell you
They will win it.
"There's top talent there and we've not even mentioned players like (Tottenham's) Ryan Mason
Now's the time to start bedding them in.
"Get them playing together and a bit of luck with injuries and I think we've got a really good chance.
"A lot of them would play for any country across Europe."
Delph signed a new four-and-a-half-year contract at Villa Park in January, ending speculation over his future with his old one due to expire at the end of the season.
But Sherwood admitted he wanted to sign the 25-year-old when he was boss at White Hart Lane.
He said: "I tried my best with Fabian
I really tried my best
I think there was a place for him there where he could have slotted in either side of Mason and (Nabil) Bentaleb
He'd cost too much money now, but he would have been a bargain then.
"I bumped into his agent in London and told him that if I was still in charge, I'd definitely want him to come
He's got more to show
When he goes past someone, he goes past them like they are not there."
Delph is likely to keep the captain's armband when Villa host Swansea in the Barclays Premier League tomorrow with Ron Vlaar still out with a calf injury.
Alan Hutton and Jack Grealish return from suspension but Aly Cissokho (groin), Kieran Richardson (calf) and Nathan Baker (knee) are out.
And with the international break coming Sherwood hopes it will aid his walking wounded and their survival battle with 16th-placed Villa three points above the drop zone.
"The break is great if we win on Saturday
It's a long time to dwell on things if you don't," he added
"I like Swansea, they don't worry about any other team
They go about it the way they do."
Source : PA
Source: PA