Senate Majority Leader Scott Fitzgerald and Walker had no comment on the letter -- requesting a border meeting -- written by Senate Minority Leader Mark Miller, but in a WTMJ, Milwaukee, interview Walker said he had no intention of meeting Miller at the Illinois-Wisconsin state line.
The Democrats fled Wisconsin last month to keep the Senate from having the quorum necessary to vote on a budget bill that would strip most public employees of most of their collective bargaining rights. The measure already has passed the House.
"The working people of Wisconsin are deeply concerned about what the future holds for their families, and for the great state they call home," the Wisconsin State Journal quoted Miller's letter as saying. "Now more than ever they are counting on us as leaders to work together to resolve our differences to move our state forward."
Last week, Senate Republicans approved the forcible detention of their Democratic colleagues.
At a 12:30 p.m. news conference, Walker and his allies said they were willing to negotiate with the Democrats, WISC-TV, Madison, reported.
Sen. Bob Jauch said he hoped Democrats would be able to go home soon.
"My wife brought me ... another two weeks of clean clothes but I told her I hoped I didn't have to use it. At some point this transition has to occur," Jauch said.
Two other Democratic senators met with Fitzgerald last week in Kenosha.
"I assure you that Democratic state senators, despite our differences and the vigorous debate we have had, remain ready and willing to find a reasonable compromise," Miller wrote.
Earlier Monday, the Democrats said they would not return to Madison "until workers' rights are preserved."
The lawmakers denied a report by The Wall Street Journal that they would return to the capital soon, saying the newspaper took a statement out of context.
The Journal said in its online edition late Sunday the fugitive senators would return to Wisconsin "in the relatively near future."
State Sen. Chris Larson of Milwaukee said in a statement the Journal took Miller's comments "out of context."
"Dems will return when collective bargaining is off the table," he said. "That could be soon, based on the growing public opposition to the bill and the recall efforts against Republicans. Unfortunately, the WSJ fished for the quote they wanted, skipping this key step in logic: We won't come back until workers' rights are preserved."
Miller said through a spokesman the Democrats were negotiating with Republicans to reach a compromise that does not strip state workers of their bargaining rights.
The standoff has drawn thousands of demonstrators to the Capitol for days at a time.