Arsenal also emerged as the fourth team to record two wins from two matches following their 1-0 win over Aston Villa at Villa Park on Monday night.
But before the game at Villa Park, Lineker said Arsenal would win the title with a 10-point gap this season.
However, the former England attacker said he had changed his mind.
He said that while Arsenal would still win the title this season, they would not do so with a gap of up to 10 points.
He believes Chelsea and Manchester City will follow the Gunners closely.
Chelsea’s attacking trio of Cole Palmer, Joao Pedro, and Morgan Rogers appears particularly formidable, having netted seven goals against Fulham and Brighton, although they have faced challenges defensively, conceding five goals.
Manchester City narrowly defeated Bournemouth in their opening match, but they returned to their dominant form on Friday night, decisively beating Crystal Palace 4-1.
Lineker told the Rest Is Football podcast: “When comparing the top attacking trios this season, it will be difficult to beat Chelsea.
“City are another strong contender. Arsenal, having won the league last season, are undoubtedly a top team, but their strengths may lie in other areas of the squad.”
He went on: “Manchester City possess significant attacking power. Enzo Maresca has made a commendable start.
“I stated last week that Arsenal would win by 10 points – I have changed my mind.
“I believe City and Chelsea could challenge them closely, but my opinion on the title remains unchanged. I still consider Arsenal to be the favourites.”
After their narrow win at Villa Park, Arsenal will host Chelsea at the Emirates Stadium on Sunday afternoon.
EPL: ‘I’ve changed my mind’ – Gary Lineker changes title prediction after Week-2 fixtures