Serie A top scorer Ciro Immobile tallied his 35th goal in Lazio's 2-0 defeat of relegated Brescia on Wednesday, leaving him one shy of the domestic overall record.
The Italian international is also eyeing the Golden Boot as Europe's best striker after striking clinically after setting up Joaquin Correa's opener.
He now has one more goal than Bayern Munich's Robert Lewandowski, who has won the German Bundesliga, while Juventus' Cristiano Ronaldo trails on 31.
Gonzalo Higuain set the current Serie A record of 36 goals with Napoli in 2016, before moving to Juventus.
"We all hope that Ciro sets the record, although there is still Cristiano Ronaldo," said coach Simone Inzaghi, who steered Lazio to secure fourth-place.
"It would be a great achievement for Ciro, for the team and us of the staff. Now he is four goals ahead. Let's see what happens."
Juve went into the penultimate round with the title already secured and suffered a 2-0 defeat at humble Cagliari, who came from a run of four losses and four draws.
AC Milan veteran Zlatan Ibrahimovic struck twice in a 4-1 win at Sampdoria, netting his second brace in the last three outings.
The 38-year-old Swede opened with an early undisturbed header and in the second half nodded to set up Hakan Calhanoglu's volley before flicking in the Devils' third as the Turkish forward returned the favour.
"Zlatan has been crucial for our improvement and his form keeps getting better," coach Stefano Pioli said about the star, who signed from January to the end of the season for a second term with Milan.
"There is a will to keep going, then I cannot say much about economic matters. He tells me he is happy and feels good here, and he shows it every day."
Milan, however, remained four points adrift of Roma, who rallied to win 3-2 at Torino and will enter the group phase of the Europa League, leaving the play-offs to the sixth-placed Devils.
Napoli are seventh but qualified through the Italian Cup success.
Roma captain Edin Dzeko, Chris Smalling and Amadou Diawara struck for the Giallorossi, who will tackle Juventus in the closing round on Saturday.
Francesco Caputo also hit a brace, for a 21-goal tally, as Sassuolo crushed 5-0 Genoa, who had coach Davide Nicola dismissed for protesting, while Lecce rallied to beat Udinese 2-1 but still remain in the three-team drop zone.
The day's third brace came from Verona's Samuel Di Carmine in a 3-0 defeat of relegated SPAL and Federico Chiesa did better with a hat-trick as Fiorentina hammered Bologna 4-0 to draw level in mid-table with their opponents and Parma.