"Why not?" Paet said in response to a question from ERR's Anvar Samost on whether Toomas Hendrik Ilves could return for a third term.

Ilves, who was head of state over two terms 2006-2016, is an example of a candidate who might have presidential contacts at the international level which, Paet says, are the keystone of Estonia's foreign and defense policy.

"Given our position and one of our less friendly neighbors, we could make better use of the resources we have," Paet said, appearing on ERR's "Otse uudistemajast" current affairs webcast Wednesday morning.

Paet, who was foreign minister between 2005 and 2014, in Andrus Ansip's, and later Taavi Rõivas' cabinets, and is now an MEP, said that personal contacts internationally enable decision-makers to showcase Estonia's concerns and interests at that level and, if necessary, to influence international decisions which affect Estonia.

"From the point of view of the presidential elections, it would be right to say that they are our foremost diplomat," Paet said of the office of president, which, for him, made it perplexing that this topic was not more in the spotlight than is currently the case.

"The domestic political dimension is certainly significant for a president, but unfortunately we are not talking about foreign policy dimensions of the president's activities whatsoever," Paet said.

"How many people do we have who are able to reach out to key decision-makers in the world? But if they can't, we can't make contacts," Paet went on.

The two coalition partners, Reform and Center, say they have at least one potential candidate in mind which they could agree on, though the individual has not been publicly named.

Kersti Kaljulaid is eligible for a second consecutive term, and has been linked with more than one high-level international job in recent months, including the position Secretary General of the Organisation for Economic Cooperation and Development (OECD which she announced she was running for last autumn, withdrawing in January this year.

More recently, news portal Politico mentioned her as a possible successor to Jens Stoltenberg as head of NATO. Stoltenberg is a former prime minister of Norway.

Kaljulaid has not declared one way or another, however.

The only two individuals to have stated an intention to run are academic Tarmo Soomere, and former Riigikogu speaker Henn Põlluaas (EKRE), who has has been traveling round Estonia presenting his candidacy.

Any potential candidate requires 21 votes at the Riiigkogu to run in the first place, and 67 or more votes at the 101-seat chamber to be elected president.

Paet said that trying to find a candidate amenable to most of the five Riigikogu parties essentially precludes the election of a politician, however.

"We're trying to find the lowest common denominator. But that's wrong, because we're wasting our opportunities," he said.

Estonian presidents may not belong to any political party and must leave any party they are a member of in order to take office.

This also presented a conundrum when it comes to potential concrete figures, in addition to Ilves, Paet said that the majority of Estonia's former prime ministers, foreign and defense ministers could be suitable.

Interviewer Anvar Samost noted that this covered quite a lot of people, to which Paet replied: "Absolutely. But in essence, all of these are excluded, as it has been stated that a politician cannot be president. A situation has been reached where politicians are out of the equation."

Outside Estonia, Paet gave the example of current German President Frank-Walter Steinmeier, who is a former foreign minister.

Article 80 of Estonia's constitution says that presidents may not have more than two consecutive terms but, unlike for instance in the U.S., more than two non-consecutive terms are permissible.

Ilves himself, however, has ruled out any third term.

In response to a question on the same posted on social media by editor-in-chief of literary periodical Sirp, Kaarel Tarand, Ilves responded: "Nope. That's all. Nope."

Former justice minister Jüri Raidla, another name recently linked with the job,  cited a lack of experience in foreign policy as one of his main reasons for declining to run.

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