Grealish, whose future has been the subject of intense speculation for the whole summer, trained at Villa's Bodymoor Heath training ground on Thursday morning and club insiders are now confident he won't be sold before the 5pm transfer deadline.
Pochettino added: "We have a very good squad, with very good players and it is very hard to add players to that".
"That is true, don't believe in £400m, that (£1bn) is the truth!"
Tottenham Hotspur became the first Premier League club since the summer transfer window began to fail to sign a single player but Mauricio Pochettino said he was happy for the club to "behave differently". That is a drama, I feel sorry for the English people.
"With Brexit it is worse because the cost is 30 percent more - that is a drama, I feel sorry for the English people - and then keeping the best players, for me [that] is to be courageous".More news: Thanks West Ham - Hammers New Boy Relishing Premier League Chance
"We believe a lot in our players and why not repeat a similar season like a year ago or the season before, and with more experience?"
It is at odds with boss Mauricio Pochettino's perceived wish, where he challenged the club to be "brave and take risks" at the end of last season. "It's a fearless decision".
The Argentine appeared at the end of last season to call on the club's owners to make some signings after Spurs finished in the Premier League top three for the third consecutive season.
The likes of Harry Kane, Dele Alli, Eric Dier, Jan Vertonghen, Kieran Trippier and Hugo Lloris only started their pre-season training over the past two weeks but Pochettino is hopeful they will be able to play some part against Newcastle on Saturday. You need to be clever in how you settle your principles, your strategy and to try to win.
"It was a unusual transfer market because I think until England was out (of the World Cup) no-one was moving". If all the players today are thinking about a collective target, we can be competitive. "That is the key this season".