City manager Roberto Mancini has been unable to satisfy the demands of all his players following another offseason spending spree that exceeded 100 million pounds ($154 million).
Despite being key players in recent years, Craig Bellamy and Stephen Ireland have already been forced out this month, while goalkeeper Shay Given has also lost his starting spot.
The 26-year-old Adebayor is pushing for a transfer a year after his signing from Arsenal was viewed as a major coup for a club that hasn't won a major trophy since 1976.
The former Togo striker played less than 10 minutes of City's opening league draw against Tottenham and watched the team produce an emphatic 3-0 victory over Liverpool without him.
Asked if he would fight for his place in the team, Adebayor told Talk Sport radio: "If you're not playing and there is a team that comes in for me then definitely I will be on my way out because I am a footballer and I love playing."
"So if I don't have a chance to play here probably there will be a lot of chance(s) to play somewhere else," Adebayor added. "I want to stay here and play, but if they force you out then you always have to follow your destiny."
The transfer window closes on Tuesday.
Although the season is only two games old, City is already in the top four, where it hopes to end the season.
The teams above City - Chelsea, Arsenal and Manchester United - are in action before them on Saturday.
Chelsea kicked its title defense with 6-0 routs of West Bromwich Albion and Wigan to lead the standings by two points. And Stoke, the visitors to Stamford Bridge on Saturday, were routed 7-0 in April.
Second-place Arsenal also produced a 6-0 rout last weekend, although the trip to Blackburn will be far tougher than a match against newcomer Blackpool.
The game may come too soon for new signing Sebastien Squillaci, but the Frenchman is ready to embrace the physicality of the Premier League.
"I am 30 and I have a bit of experience - now I am going to discover a new league," the former Sevilla defender said. "I do like the duels. I feel it is one of my qualities and here in England there are many duels and it is good to be able to respond physically."
Manchester United will host West Ham looking to recover from Sunday's setback at Fulham, when the 18-time champions conceded a late equalizer after Nani missed a penalty.
Confidence is high at Tottenham, which plays Wigan on Saturday after beating Young Boys 4-0 to qualify for the Champions League for the first time.
Having dropped out of the top four last season at Tottenham's expense, Liverpool is still without a win in the new campaign - collecting just one point from a possible six.
West Brom, though, should prove to be less challenging opponents than Arsenal and Manchester City.
Liverpool's preparations have been boosted by forward Dirk Kuyt committing his future to the club as Javier Mascherano prepared to join Barcelona.
While Liverpool qualified for the group stage of the Europa League on Thursday, Aston Villa lost its playoff, piling the pressure on interim manager Kevin MacDonald going into Sunday's home match against Everton.
"With the uncertainty of the manager (situation), it is difficult," Villa captain Villa Stiliyan Petrov said. "It would be nice to see who is going to be appointed, who is going to take charge."
Also on Saturday, Blackpool plays its first home match in the Premier League when Fulham travels to the northwest, while Newcastle, which beat Villa 6-0 on Sunday, goes to Wolverhampton.
On Sunday, Bolton and Birmingham, who have both won one and drawn one, meet at the Reebok Stadium.
