Shearer was brought in to take over from caretaker managers Chris Hughton and Colin Calderwood, who assumed responsibility after interim boss Joe Kinnear was forced to stand down with health problems.
And with Kinnear's contract expiring at the end of the season anyway, Llambias said the club were keen to tie Shearer down to a long-term deal.
"We want him to be the manager 110%," he said.
"He's very good at what he does and he's a straight-talking guy - we like that. He would be the perfect appointment.
"We are trying to sort something and we will give the public some information as soon as possible.
"Alan has put a lot of work into the job at Newcastle and we are talking to him now."
Saturday's loss at Aston Villa ended a 16-year stay in the Premier League and BBC Radio 5 Live's senior football reporter Ian Dennis said: "If Shearer gets certain assurances then he would be happy to take over full time.
"A decision also needs to be made over the playing squad because it's only five weeks before pre-season starts on 1 July."
Meanwhile, former chairman Sir John Hall has branded the club's relegated playing staff as "useless".
Hall's money helped Newcastle climb up from the second tier of football back in 1993 before he sold his shares to Ashley in 2007.
Michael Owen - he's had too many injuries and he's never seemed to be on the ball
Former Magpies chairman Sir John Hall
"The table doesn't lie," he told The Sun newspaper.
"It's been desperately poor all season and the worst thing is they didn't even appear to try on Sunday.
"I'm not going to pull any punches. This current side is rubbish. Useless."
But Hall firmly believes Shearer is the right man to guide Newcastle back into the top flight.
"Shearer must stay," he stated. "He doesn't have experience but then neither did Kevin Keegan the first time round.
"But, like Keegan, the fans have faith in him. The club is in his blood and he is a rallying point for all the supporters."
Shepherd points finger at Newcastle owner
Meanwhile, Freddy Shepherd who took over as chairman from Hall before Ashley's buy-out, said Newcastle's relegation was "terrible" for the supporters.
"We were there for 16 years," Shepherd told the BBC.
"To lose Premier League status is huge. It's terrible for the supporters and I feel sorry for them.
"Everybody in world watches Premier League football but now they won't be able to watch Newcastle."
Regarding reports that he was set to front a takeover of the Magpies: "The club was taken off market, but we'll see what happens."
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