"After 15 minutes, he said to me he wants to stay and play for Chelsea for many years. I think Chelsea needs Lampard. I think Lampard is with us more time than one year.''
No financial offer was made for Lampard, Chelsea added on its website.
Lampard has been persistently linked with Inter, which is now coached by former Chelsea manager Jose Mourinho.
Mourinho has already said Lampard is likely to join him, whether that is during this offseason or on a free transfer when his contract expires.
"Lampard is one, just one, of our targets,'' Inter official Ernesto Paolillo revealed to the British media.
"If he comes he will be welcome.
"Of course it is always a question between quality and price. If it is not possible to reach Lampard, we will try something else.''
Drogba 'happy'
Scolari is also aiming to keep Didier Drogba at the club, with AC Milan and FC Barcelona both reported to be interested in the Ivory Coast striker.
Since Mourinho left last year, Drogba has repeatedly suggested that he will quit the Blues, but Scolari wants the player in his squad as he tries to wrest the Premier League and Champions League titles from Manchester United.
"One hundred percent. No, not 100, 200 percent,'' Scolari said. "I like him.''
Scolari, who said he had previously voted for both Drogba and Chelsea captain John Terry in Fifa's world player of the year poll, added that he had already seen Drogba at Chelsea's training ground.
"I saw him happy,'' Scolari said.
Scolari said he was also pleased that England internationals Ashley Cole and Joe Cole had reported early for preseason training so they could have treatment on minor injuries before starting.
Unsurprisingly, given Scolari's previous admiration, Terry is set to continue as Chelsea captain despite uncertainty regarding his same role with England.
"I like him as a captain. I like him as a player, as a leader,'' Scolari said.
"He came to my room and said, 'I am John Terry.'
"I said, 'I know you.'''