Among the most prominent ones making the rounds was a potential trade with the Brewers, an organization Mariners general manager Jack Zduriencik knows extremely well.
Washburn is perhaps the Mariners' most marketable player and fits the rent-a-player concept. He is in the final year of his four-year contract and is having one of the best seasons of his career, posting an 8-6 record and 2.71 ERA in 19 starts.
But as of late Monday afternoon, it didn't appear that anything was imminent.
"Obviously there's a lot going on," Zduriencik said before the Mariners' series opener against the Jays. "A lot of people anticipate things. We try to improve our club all the time, whether it's internally or we go outside. Our focus right now, after this weekend, is to just try to get back on track and get back on our winning ways.
"With Felix [Hernandez] today and 'Wash' tomorrow, we have a chance to do that. We'll see what happens. I think you take it a day at a time and give it your best shot. This club has been resilient; they've bounced back."
While the Mariners might be down after being swept and outscored 31-6 during the three games against the Indians, Washburn insisted they are not out of the race they had worked so hard to stay in.
"It definitely wasn't a good weekend, but [the 7 1/2-game deficit] isn't insurmountable," he said. "There are two months left. The Angels and Rangers are due to cool off and go through a stretch like we did the last three days, and it would be better sooner rather than later. Both teams have been hot and have played good baseball, but hopefully they will cool off and we can catch them. There is a lot of baseball left. We are looking up, but by no means is our season over."
But the trade rumors continue to swirl around the team, in general, and Washburn specifically.
"My dad called me and said, 'Did you get traded to the Brewers?'" Washburn said. "I said, 'Dad, don't you think I would have called you if something had happened?' I followed up with, 'Don't you remember what happened last year?' All the times I supposedly got traded, and nothing happened. You get a lot of calls and text messages from people wondering what's going on. I tell them all the same thing: I will let you know if something happens."
The Mariners were known to have discussed Washburn with the Yankees and Twins last season, and he would have welcomed a swap to either team, especially the Twins, the closest Major League team to his offseason home in Wisconsin.
He's not nearly as anxious to change business addresses this season and has even discussed a willingness to sign a contract extension with Seattle.
"That would be something I definitely would be open to," Washburn said. "I love pitching in Seattle, my family loves Seattle and I have expressed that [a new contract] would be something I would be open to. If they wanted to go that route, I would definitely be willing to listen.
"It was different last year because we were definitely out of [playoff] contention," he added. "This year, I don't think the season is over with here. We had a tough weekend, but it's not over. I wouldn't be disappointed to stay a Seattle Mariner. I would be happy to be a part of this group of guys, forget about last weekend and return to playing good baseball like we did before those three games."
And he would also like to get back to a "normal" routine.
"A starting pitcher is supposed get talked about once every five days, not every day," Washburn said. "We're used to kind of hiding back in the shadows until it's our day to pitch, so this is different for us to have to answer questions every day and get talked about every day. It's out of the norm."