Toyota have offered Kimi Raikkonen a deal for next season but the 2007 Formula One champion's management wants more, according to the team's motorsport president John Howett.
"We don't play too many games. We put on the table what we can afford and what we think is a serious offer in the current market," Howett said after Sunday's Brazilian Grand Prix.
"I think genuinely we could work well with him, give him a car that's quick."
Raikkonen will be replaced at Ferrari by double world champion Fernando Alonso at the end of the season and has yet to decide what to do next, although a return to his former employers McLaren appears his most likely option.
The party-loving Finn has said he wants to be in a competitive car, and Toyota have yet to win a race since they entered the sport in 2002.
Howett said Raikkonen could be a good fit for a manufacturer who came to Formula One after winning rallying world championships.
"We have had very good relationships with Scandinavian drivers in the rallying times that enjoy life and it works very well, so we could cope with it as a team," he said.
Poland's Robert Kubica was another target for Toyota until he signed with Renault. The Japanese team, whose future in the sport remains subject to considerable paddock speculation, currently have Italian Jarno Trulli and Germany's Timo Glock under contract.
"With both drivers we are still maintaining a degree of discussion," said Howett.
"We have put an offer on the table with Jarno, I think that he himself is not dissatisfied with the financial offer, the bottom line to some extent is certain issues on the contract and I don't think they are negotiable from our side.
"He may well be in the car next year but it's not at all clear."
Japan's Kamui Kobayashi made his race debut for Toyota at Interlagos, standing in for the injured Glock and making a strong impression when he ran as high as third place while fending off championship winner Jenson Button for several laps.
"I thought he defended well, he re-took Jenson," said Howett. "He's fearless and did a good job to get past Fisichella.
"He was a bit off the pace overall but it was very impressive. You have to say we have to give him serious consideration but still pace-wise he was a bit slow so we have to see."
Button was less complimentary of the debutant: "I tell you, that guy is crazy, crazy," he told reporters. "I suppose it is just inexperience but he moves a lot in the braking zones which makes it very difficult."