Although he is not on an NFL roster Sunday, there is every reason to believe that former New York Giants cornerback Janoris Jenkins will be playing as soon as next weekend, and likely for a playoff contender, league sources told ESPN.

The bigger questions are whether Jenkins will clear waivers Monday or Tuesday, and how much money he will make.

If Jenkins clears waivers Monday as an injured player -- he has been nursing a minor ankle injury -- he would revert to the Giants' injured reserve list. But the Giants also could waive him off it, which they would be expected to do, meaning Jenkins would go on waivers a second time from Monday to Tuesday.

League sources believe that a playoff contender that has a need at cornerback, such as the Houston Texans or Kansas City Chiefs, could put in a claim or try to sign him after he clears waivers, according to sources. Any team that claims Jenkins would owe him two weeks of salary at $597,000 per week -- just under $1.2 million for the remainder of this season, along with a 2020 contract that is scheduled to pay him $11.25 million.

For now, Jenkins doesn't know whether he will clear waivers Monday, clear waivers Tuesday, be claimed by another team or have his choice of teams to sign with on Tuesday.

But the belief is that despite nursing an ankle sprain, Jenkins could be in a new locker room and back on the field as soon as next weekend.

The Giants waived Jenkins on Friday, two days after he made an inappropriate remark to a fan on Twitter. Jenkins called a critical fan a "retard" when taking exception to questioning about why the stats Jenkins was using to showcase his effectiveness weren't contributing to victories.

Jenkins said Thursday that the usage of the word was "slang" that is "just part of my culture." Giants coach Pat Shurmur met with Jenkins on Wednesday and said in a statement Friday that Jenkins' refusal to admit that what he did was wrong led to his release.

ESPN's Jordan Raanan contributed to this report.