The short break since the last race in Germany earlier this month has not provided any answers as to whom will replace Mark Webber at Red Bull at the end of this season.
The only change to the situation is that Jean-Eric Vergne appears to be have fallen by the wayside and it is now a two-horse race between the Frenchman's Toro Rosso team-mate Daniel Ricciardo and Raikkonen.
Red Bull have made it clear they hope to make an announcement by the end of next month, while Raikkonen has stated he is in no hurry to decide on his future.
Ahead of this weekend's Hungarian Grand Prix, Boullier said: "It's clear Lotus is a desirable place to be.
"We know there's been a lot of talk about Kimi's future, and we all know Kimi is an individual and he will make his decision in his own time.
"Naturally, we want him to continue in the sport and continue with Lotus, so we're doing everything we can do to make that happen."
Raikkonen goes into Sunday's race at the Hungaroring trailing series leader Sebastian Vettel by 41 points, with Ferrari's Fernando Alonso seven points ahead of the Finn.
The venue has been a happy hunting ground for Raikkonen over the years, although after finishing runner-up on four occasions and winning once, he concedes he has been "second too many times".
But with temperatures poised to hit 30 degrees centigrade in Budapest this weekend, and with this season's Lotus proving adept in the heat, another win is on the cards.
After finishing just one second behind Vettel at the Nurburgring last time out, Raikkonen said: "The points were good and we had a strong car.
"Again we saw warmer temperatures suited us, and we usually get hot weather in Budapest so that should be a good thing.
"The heat has helped us with the car so far this year so that will make things better, but only if it's a win will you not suffer from the heat."
This weekend marks the debut of Pirelli's new tyres, which were given a workout over the three days of the young driver test at Silverstone last week.
Following a series of high-speed blowouts during the British Grand Prix, Pirelli was forced to revise its rubber.
From this weekend the tyres comprise last year's construction with this year's compounds, with Boullier believing the worst is behind Pirelli.
Boullier said: "It was good for us to get some mileage in lovely conditions at Silverstone.
"We were able to utilise Nico (Prost) and Davide (Valsecchi) to run the type of programme we haven't been able to implement over the past few seasons where the young driver test occurred at the end of the year.
"We did intend to run Kimi, but when the limitations on what race drivers could do in their testing for Pirelli became evident, it made more sense to be able to run a normal test programme with Nico.
"Budapest will be the real test, but we're confident we have enough data to say there shouldn't be any nasty surprises."
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