Newcastle have avoided defeat in their first five matches in all competitions since Jaissle took charge during the European summer, giving the new manager an encouraging start at St James' Park.
Their latest success came in the Carabao Cup, where Joe Willock's 81st-minute goal secured a 1-0 victory over Millwall and a place in the next round.
Jaissle knows the challenge will increase against Leeds, but he wants Newcastle to approach the game with ambition.
"We are happy for the start we had, definitely it's not normal after being just such a short amount of time together, but Premier League is Premier League," Jaissle said.
"We face every matchday top opponents. Now against Leeds it will be tough, away match against a strong one.
"We want to continue the journey, of course, be ambitious like I've said many times, but also we are realistic."
The Newcastle manager has also been impressed by Lewis Hall, who has established himself as an important part of his plans after attracting transfer interest during the summer.
Hall has now committed his future to Newcastle by signing a new long-term contract, with Manchester United among the clubs reported to have shown interest in the England international.
Jaissle believes the left-back still has plenty of room to develop.
"Without speaking about his contract, I can just say that I'm in love with what I've seen so far from him," he said.
"It's an amazing player with huge potential still, and this makes me so happy to, hopefully, have him here for the next years in the long term.
"He's fitting so good to this identity, how we want to play football, and again, he's doing an excellent job."
Hall was equally pleased to extend his stay at Newcastle and highlighted the importance of representing the club and its supporters.
"I'm absolutely delighted. It's a really proud moment," Hall said.
"It's an absolute pleasure to play for this club and to represent the supporters. I know how much it means to them."
Hall also pointed to his family connection with Newcastle as another reason why the new contract means so much to him.
"I obviously have a family connection with the club, which is incredibly important to us all," he said.
"One of the main reasons I play is to make my family proud, and I know how much it means to them to watch me playing for Newcastle United."
With Newcastle unbeaten under Jaissle and Hall committed to the club for the long term, the defender believes there is plenty of reason for optimism.
"It's really pleasing with how we've started the season, especially with the new gaffer and coaching staff coming in, and I think we can go on to achieve really big things," Hall said.