Šadurskis said in an interview with BNS on Saturday that he has met with President Raimonds Vejonis but did not answer the question whether Vejonis has offered him the position of the prime minister.
Šadurskis said that they had agreed with the president not to disclose the subject of their negotiation. He said that more news on the issue would be released on Tuesday.
So far the president has addressed Finance Minister Janis Reirs and Valmiera city mayor Janis Baiks, both of whom turned the offer down.
Though Šadurskis is seen as a likely nominee, confirmation is by no means certain with both the Greens and Farmers Union (ZZS) party, which is one of three in government, saying it would not be particularly happy with him in the PM post.
ZZS parliament faction head Augusts Brigmanis in an interview with the Latvian public television on Monday said that ZZS has not spoken with Sadurskis as the candidate for the prime minister, and President Raimonds Vejonis has not officially nominated him.
Brigmanis said that ZZS would like to hear why Sadurskis has agreed to run for the position, being an unpopular politician, and how he plans to win public support.
Asked whether ZZS might name its candidate for the prime minister, Brigmanis said: "Time will tell," suggestive that Šadurskis could win ZZS' backing - at a price.
Nor is Šadurskis universally popular among his own Unity party, seen as he is as coming from the party's right wing.
President Vejonis has been holding meetings with potential candidates for prime minister. The talks have been taking place behind closed doors. Latvia's outgoing Prime Minister Laimdota Straujuma announced her resignation on Dec. 7.