Jon Lester could sign a contract with a new team before the week is over.

There is, however, no deadline in place for the free-agent left-hander to come to terms on a deal, according to source.

Lester is reportedly choosing between the Boston Red Sox, Chicago Cubs, San Francisco Giants and maybe even another team or two that hasn't been reported.

Through Wednesday afternoon, Lester had met with the Red Sox, Cubs, Giants and Atlanta Braves.