The phrase "asserted that it is possible" is correct and usable in written English.
You can use it when you want to indicate that someone has confidently stated or claimed the possibility of something.
Example: "The scientist asserted that it is possible to reverse climate change with the right technologies."
Alternatives: "claimed that it is feasible" or "stated that it can be done."
Nevertheless, Norinaga asserted that it was possible and rewrote the Kojiki: against the Chinese characters of the original text, he rewrote the Kojiki in what he claimed was the ancient language using kana (the Japanase syllabary).
"There are some who, as we said, both themselves assert that it is possible for the same thing to be and not to be, and say that people can judge this to be the case.
Take 33a as an example, hai asserts that it is possible that she ate chocolate (i.e., the focused denotation) and it is possible that she ate cookies (i.e., the alternatives).
Piketty seems to assert that it is possible (starting from here) to greatly increase the value of society's capital without, at the same time, greatly increasing its income.
Although SE doesn't have yet specialized and widely adequate sources of sampling for subjects recruitment, we assert that it is possible to reduce the population bias and enlarge samples in SE surveys whether a systematic recruitment is planed over a professional social network and its results are analyzed through probabilistic sampling methods.
This emerging evidence has led to a recent joint science advisory statement by the American Heart Association, The American Cancer Society and the American Urological Association asserting that it is possible that ADT could increase cardiovascular risk on the basis of its adverse impact on risk factors (Levine et al, 2010).
Today he is remembered for preaching optimism and personal fulfillment, asserting that it was possible to achieve spiritual and material success in life.
"One more link in a long chain of American entitlement". This is a radical book because it challenges the conventional wisdom that self-defense and punitive systems are the only way to keep ourselves physically and emotionally safe, and, maybe more important, because it asserts that it's possible to work for the betterment of society without the accompanying side effect of feeling like a chump.
