Previews: Milan racing to seal Zlatan deal
Milan, third last term, have struggled for goals in warm-up matches under new coach Massimiliano Allegri so the club are looking to bring the former Inter striker back to Italy despite their frugal transfer spending.
Chief executive Adriano Galliani, who watched Wednesday's defeat on penalties in a friendly with Barcelona, has stayed on in the city and will try to secure a two-year loan despite speculation Barca only want to sell.
"I'm trying and that's why I am here, I will not move, even if it means not going to Milan against Lecce on Sunday," Galliani told Milan's TV channel.
"I will do all that is in my ability to try to bring this great champion to Milan. It is very difficult."
If a deal is not done in time then Marco Borriello is set to lead the line on Sunday.
AS Roma, runners-up last term, start their campaign at home to promoted Cesena on Saturday but main new signing Adriano is likely to miss the early weeks of the season with a muscle problem after the club said he had gone for tests.
Juventus and a raft of new buys visit Bari in Sunday's early game with the rest of the day's programme in the evening rather than the traditional afternoon because of the heat.
A dismal seventh last season, Juve are trying to wrap up a deal for Udinese striker Antonio Di Natale in time for Sunday with Diego and David Trezeguet on the verge of leaving the club.
Champions Inter Milan are not in league action until Monday at Bologna because they face Atletico Madrid in Friday's European Super Cup.
New coach Rafael Benitez, who made a confident start to replacing treble winner Jose Mourinho by clinching last weekend's Italian Super Cup against Roma, could well rotate his side slightly given the two games come so close.
The new Serie A season offers several innovations including television cameras in the dressing room before kickoff and the use of electronic cards for fans to enter matches.
The new cards are unpopular with fans who feel the government's effort to track hooligans is too draconian and minor violence has flared during supporter protests.