Conte's Inter host the southerners -- back after a seven-year absence from the top flight -- looking to match Juventus and Napoli who both won their openers on Saturday.
"Obviously there's still a gap (on Juventus and Napoli) but the chase is on," Conte told a press conference on Sunday.
"We are working in the right way, there is a desire to build something important."
Inter last won Serie A in 2010 under Jose Mourinho, and have been remodelled by former Italy boss Conte, who replaced Luciano Spalletti after the Chinese-owned club finish fourth last season.
Conte coached Juventus to three Serie A titles in a row from 2012 to 2014, and won the Premier League with Chelsea in 2017.
Belgian forward Romelu Lukaku was Inter's star signing of the summer from Manchester United for 65 million euros ($73 million).
"Romelu has arrived full of enthusiasm, he's a bright lad and he's done well to fit in right away," said Conte.
"He made himself available immediately and he's working hard.
"He's joined after a spell on the margins at Manchester United, therefore, he has huge margins for growth from every perspective.
"He's an important player with great potential considering he's only 26."
Uncertainty remains however over the future of Argentine forward Mauro Icardi who remains in conflict with the team and lost the captain's armband last season.
"I have great respect for everyone, but from my point of view I don't feel any disturbance," said Conte of Icardi's presence.
"We are working hard, we know full well what approach has been taken with the player, but it is not causing any disturbance for me."
The match will be a special one for 50-year-old Conte who was born in Lecce, in the heel of Italy.
"I was born in Lecce and it’s a city that I have in my heart," said the former midfielder, who played for the team for six years before moving to Juventus where he won 13 trophies including five Serie A and the Champions League title in 1996.
"Obviously, it'll be an interesting game and I'm pleased to be facing Lecce in Serie A," he said.
"It'll be a great match with many strong connections, although inevitably they'll be our opponents tomorrow."
Inter have won 14 of their 15 home Serie A matches against Lecce, outscoring them 43-6 in those matches.
Lecce's only win at the San Siro was a 1-0 success back in November 2000.