The 65-year-old has been in control of the Biancocelesti reins since the summer of 2021, during which time he has taken charge of 137 matches, but his side are on a dire run of form.
Lazio had already lost three successive games heading into Monday's clash with Udinese, going down to Fiorentina and AC Milan in Serie A action before a 3-0 loss to Bayern Munich in the Champions League, which saw them bow out of the last 16 3-1 on aggregate.
A frenetic four-minute period at Stadio Olimpico on Monday saw Lorenzo Lucca and Oier Zarraga net for Udinese either side of a Lautaro Giannetti own goal, thus condemning Sarri's side to a fourth straight defeat in all tournaments.
No other team in the division has lost each of their last three games, and the Biancocelesti - who also lost to Atalanta BC and Bologna in February - are now languishing in ninth place in the table, eight points off the top five and a staggering 35 behind leaders Inter Milan.
According to La Gazzetta dello Sport, Sarri - whose contract at Stadio Olimpico runs until 2025 - immediately emptied his locker and announced his intention to resign when he arrived for work on Tuesday morning.
Lazio have apparently been left shocked by the timing of Sarri's resignation, but club president Claudio Lotito must still accept the Italian's exit before the former Chelsea and Juventus coach officially leaves the club.
Lotito is expected to agree to Sarri's resignation, which will see the 65-year-old depart with 65 wins, 30 draws and 42 losses from his time at the helm, averaging 1.64 points per game.
Sarri led Lazio back into the Champions League with a second-placed Serie A finish in the 2022-23 campaign, finishing 16 points behind champions Napoli, but he has failed to deliver a piece of silverware to the Biancocelesti faithful.
Should Lotito give the green light to Sarri's exit, Lazio will be expected to appoint an interim manager until the end of the season and are said to be considering former striker Miroslav Klose as a potential candidate.
The 45-year-old German hung up his boots in 2016 after a five-year spell in sky blue and took on his first managerial role with Austrian side SCR Altach last year, but he left midway through the season with just five wins from 24 games.
Another ex-forward, Tommaso Rocchi - who previously managed Lazio's youth teams - is also under consideration, as is Igor Tudor, but the latter would demand a multi-year contract rather than a short-term appointment until June.