The 31-year-old goalkeeper has been one of the best players at the Euro 2016 finals so far and has been a key figure in Northern Ireland’s successful campaign.
Washington has spoken highly of the former Celtic prospect, and has backed him to find a new club soon.
“He's a great guy and a quality goalkeeper,” the QPR striker told the club’s official website about McGovern. “He’s out of contract this summer, but I'm sure he won't be short of suitors after his performances so far.
“He also deservedly made it into the team of the group stage which is great for him to get that recognition.”
Former Leeds United and Queens Park Rangers manager Neil Warnock has also backed McGovern to get a good move in the summer transfer window once he returns from international duty with Northern Ireland.
“Michael McGovern, he has got a right chance of getting a good move now his contract’s up at Hamilton,” said Warnock on The Alan Brazil Sports Breakfast show on talkSPORT on Friday morning (broadcast from 6am, June 24).
McGovern has kept one clean sheet in three matches for Northern Ireland at the 2016 European Championship so far, making 4.33 saves per game and 6.50 saves per goal in average in the process.
According to a recent report in The Scottish Sun, Premier League side Southampton and Championship outfit Rotherham United are interested in signing the former Falkirk goalkeeper in the summer transfer window.
The Sunday Post reported earlier this month that Scottish Premiership-bound Glasgow Rangers are looking at McGovern.
However, the recent signing of former Burnley goalkeeper Matt Gilks on a free transfer suggests that the Gers are not going to pursue McGovern any longer.