The 38-year-old Norwegian emerged as a surprise candidate for the post following the Northern Irishman's departure two weeks ago.
High-profile names such as Henrik Larsson, Owen Coyle and Steve Clarke were all linked to the job while former Celtic and Manchester United midfielder Roy Keane asked not to be considered after initial talks with the Scottish champions.
Speaking at the media conference at Celtic Park today where Deila, who guided Stromsgodset to their first title in 43 years last season, was confirmed as the new Hoops boss, Lawwell said: "Neil mentioned in an interview today that when (former assistant) Johan (Mjallby) left we had a chat about Ronny in terms of if he could play a role here.
"When Neil decided to go and the process started two weeks ago, Ronny was at the top of the list to go and have a chat to.
"Things came to a head only in the last day.
"We were in Norway yesterday and this morning he (Deila) got to talk about his own terms and conditions.
"There were no job offers (to other candidates).
"We spoke to a lot of people at different stages and got to different levels but no offer was made to anyone else."
Lawwell outlined his expectations of Deila whose first competitive match in charge of Celtic will be a Champions League qualifier next month.
He said: "We feel that we are the dominant team in Scotland at the moment and we want to continue that dominance and also take Celtic as far as we can in the Champions League.
"Also our fans demand entertaining football so we want to play expansive, winning, entertaining football, the way he has done in Norway."