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NEW YORK – With a pivotal week of talks upcoming, baseball players hope there’s enough progress in negotiations to make setting a strike deadline unnecessary. 

The union’s executive board will meet by telephone conference call Tuesday, but a decision on setting a strike date is unlikely then, two people familiar with the union’s deliberations said Friday on the condition they not be identified. 

A strike date would have to be set by the executive board and, so far, union head Donald Fehr has held off calling a meeting. If he does, the likeliest date is Aug. 12, when only five games are scheduled. 

“I was told that, hopefully, we won’t get to that meeting,” Tampa Bay player representative John Flaherty said. “That’s as optimistic as I’ve heard since we had a meeting with Don in Baltimore last year. This is the most optimistic I’ve been since that time.” 

Rob Manfred, the owners’ top labor lawyer, said there was “a mutually shared goal of getting an agreement as quickly as possible” and that “there is plenty of time to reach an agreement now. Time is not an issue.” 

For now, players don’t want to use their biggest weapon — a strike. 

“A strike date does create time pressure,” Manfred said. “People are making genuine efforts to get to an agreement without the need for that.” 

The sides plan to be available for meetings every day next week, continuing the intensified schedule that began Monday. 

“Everything is moving along in a positive matter. We feel progress is being made,” Milwaukee player representative Ray King said. “The main talk has been the steroid issue. It has been discussed as much as revenue. A lot of guys are in favor of having tests.” 

Fehr has refused to characterize recent talks, saying he won’t be able to tell if progress has been made until “after it’s over.” 

Following Friday’s two-hour bargaining session, Manfred said he expects a proposal from the union next week on management’s desire for mandatory random drug testing, which the union has opposed on privacy grounds. 

Players made a counterproposal on the minimum salary and benefits, which both sides called positive. Afterward, Manfred gave his capsulized summary of chief issues: 

“Benefit plan, minimum salary, I’m very close. On the topic of revenue sharing, we have made a lot of progress. We need to make a little more. On the luxury tax, I’ve got a long way to go.” 

Owners originally proposed an increase in the amount of shared locally generated revenue from 20 percent to 50 percent, and they also asked for a new distribution system that would favor teams with revenue close to the industry average. 

Players proposed an increase to 22.5 percent and wanted to continue the current system, which gives extra money to low-revenue teams. 

The difference in those plans was $70 million annually, using 2001 announced figures. 

“The issue is a lot more complicated than that $70 million,” Manfred said. “That’s like trying to characterize the Constitution with ‘We the people.’ It’s the tip of the iceberg.” 

The sides have moved since their original proposals, both in dollars and format. “We have made substantial progress toward each other,” Manfred said. 

The owners’ desire for a luxury tax that would slow payroll growth appears to be the last issue to be addressed. Owners asked for a 50 percent tax on the portions of payrolls over $98 million, a figure that includes 40-man rosters and benefits. 

“We can’t reach an agreement without the luxury tax being addressed,” Manfred said.