The 36-year-old limped off in the first half of Wednesday’s 3-0 win over Switzerland in Rome that put the Azzurri through to the next round with a game to spare.
Chiellini pulled a flexor muscle in his left leg but tests carried out on Thursday did not reveal too serious an injury, the sources said.
If the 109-times capped Juventus defender cannot play against Wales on Sunday, “the goal remains for him to recover for the next matches”, and in particular for the last 16, a source said.
Roberto Mancini’s side are top of Group A after beating Turkey and Switzerland.
Italy will advance as group winners if they avoid defeat against surprise Euro 2016 semi-finalists Wales at the Stadio Olimpico on Sunday.
They will play the last 16 on June 26 in London or Amsterdam depending on whether they finish first or second in the group.