PHOENIX -- In the strongest indication yet of the Red Sox’s interest in re-signing pitcher Jon Lester, team ownership is planning to meet with Lester and his agents, Seth and Sam Levinson, perhaps as soon as the end of the week.

Seth Levinson said Wednesday that he has been in touch with Red Sox owners, attempting to arrange a meeting in the next several days. Lester also has meetings scheduled with other clubs next week, but the Red Sox will have a chance, in advance of Lester’s meetings with other clubs, to launch a preemptive strike and persuade Lester of how much they want him back.

It seems Sox ownership will have a chance to show Jon Lester their level of interest in signing him. Steven Bisig/USA TODAY Sports

A meeting with ownership should make it clear whether the Sox are indeed serious about Lester or instead will turn from him to pursue other alternatives.

Is it possible they could strike an agreement immediately? Lester may feel an obligation to visit with other clubs, including the Chicago Cubs, that have expressed their interest -- in fact, ESPN Chicago reports Lester will meet with the Cubs in Chicago sometime next week.

But a quick deal with the Red Sox cannot be ruled out altogether. The Sox have never made an offer beyond the four-year, $70 million one they made in mid-March last spring, but sources with direct knowledge of the Sox offseason plans say that Boston may be prepared to offer as many as six years for Lester, with one source speculating the bid could reach the $132 million threshold.

“Something will have to give soon,” Seth Levinson said, regarding Boston’s interest in the ace left-hander, who turns 31 in January.

Red Sox general manager Ben Cherington met at some length with the Levinsons on Tuesday night, but the GM termed it more a “social visit” than anything else.

The Levinsons have prepared a 221-page, full-color portfolio on Lester that they are presenting to clubs, along with a three-minute video that makes their case that Lester matches up favorably with left-handed aces throughout history (going back to Warren Spahn and Carl Hubbell). It also focuses on his charity work and his stellar record as a postseason performer. The report relies on statistically driven websites such as fangraphs.com to show he ranks among the best pitchers in the game in the quality of three pitches (top 15 in all three) and in his ability to induce swings and misses, ground balls and weak contact.

Both Lester and Seth Levinson have said repeatedly they are not seeking to set records in the market in terms of contract size, but are looking for what they perceive as fair market value.

The meeting with ownership will be held at a location to be determined, outside of Boston.

“When it advances to that stage, I want Jon present with all clubs,” Seth Levinson wrote in an e-mail. “The strength of his character speaks to his greatness on the field and why any team would want him to be the face of the franchise off the field. . . . There is nothing stronger than to be in the same room with Jon.”