PHILADELPHIA -- Free-agent outfielder Jermaine Dye said Monday afternoon that the Nationals made him a contract offer, but it wasn't enough to uproot his family from Arizona to Washington.

Dye did not say how much money was offered to him, and Nationals general manager Mike Rizzo declined comment on whether the team offered the right-handed-hitting slugger a contract.

The team had interest in Dye since it released right fielder Elijah Dukes in late March. One source close to the Nationals felt $4 million was a fair price for Dye, who made $11 million last year with the White Sox. Washington is platooning Willie Harris and Willy Taveras in right field.

"I'm sure it was as much as they could do," said Dye about Washington's offer. "With the economy, they can only offer so much. I'm sure with that team and that payroll, what they had to offer was their best. I look at the whole situation: Living in Phoenix, Arizona -- this will be my [15th] year in the big leagues -- and Washington being on the East Coast, that's not like one of the first teams that is going to jump out at me.

"I'm not going to take my family all the way to Washington. With the offer that they made, it would maybe have to be a little bit more than other clubs have offered me in the past. I'm just not going to take my family all the way to Washington just to play.

Dye, 35, is coming off a season in which he hit .250 with 27 home runs and 81 RBIs. Dye said he has been offered deals in the $1 million range and some teams have indicated he could be a fourth outfielder.

'When you get offers from a lot of teams that are in the $1 million range, that's a negative in itself, no matter what," Dye said. "I definitely want to play. I'm working out, staying in shape and just wait for the right situation. [My family and I] are OK with it."

Flores' right shoulder improving

PHILADELPHIA -- Nationals catcher Jesus Flores, recovering from right labrum surgery, was cleared by Dr. James Andrews to start a throwing program, which starts Tuesday.

The throwing session is expected to last four to six weeks. During that period, the team is hoping Flores can swing a bat.

There is no timetable as to when Flores will return to action. He is working out at Washington's Spring Training complex in Viera, Fla.

"It's a step in the right direction," general manager Mike Rizzo said.

Flores missed most of the 2009 season because of a right shoulder contusion. Flores hurt the shoulder May 9, when he was hit by D-backs outfielder Chris Young's foul tip in Phoenix. Flores was in pain for several minutes, but he remained in the game before being taken out in the ninth inning.

Flores was activated from the disabled list Sept. 4 and made two pinch-hitting appearances. However, he was sent to Alabama after complaining of shoulder soreness and eventually has right labrum surgery performed by Andrews.

Flores didn't play a Spring Training game because the shoulder was still bothering him. He spent almost two weeks this spring rehabbing the shoulder in Birmingham, Ala., where Andrews is located.

Zimmerman close to being ready?

PHILADELPHIA -- Nationals third baseman Ryan Zimmerman was out of the lineup Monday for the second consecutive game because of a tight left hamstring.

With the day off Tuesday, the Nationals are hoping Zimmerman can play Wednesday night at Citizens Bank Park.

Guzman may see time at third base

PHILADELPHIA -- Nationals manager Jim Riggleman hopes to have Cristian Guzman play third base soon. Guzman has played one game at the position, in the 2008 All-Star Game.