Silva announced his farewell on Monday in an emotional video message on Chelsea's website
The 'Red Devils' haven't tasted defeat in their last 15 matches in all competitions and they are coming into the Bournemouth clash on the back of a comprehensive 3-0 victory over Brighton.
United remain fifth on the Premier League table with 52 points, two points behind Chelsea and three points behind Leicester, who are at the fourth and third spots respectively.
Solksjaer, however, stated their last few matches of the season won't be easy, considering they lost points against them in the reverse fixtures earlier in the season, so they cannot let their guard down against the teams who are below them in the league table.
'I've seen lots of quotes we have an easy run-in but next five games: Bournemouth we lost there this season, Aston Villa we drew at Old Trafford, Southampton we drew to, we lost to Palace, lost to West Ham," Solksjaer told reporters as per Daily Mail.
"There are teams we've got a point to prove against and we have to improve on the last performance.
"It's not an easy game, whatever anyone thinks doesn't matter, we'll have to perform. Bournemouth are fighting relegation, it's not a nice place to be," he added.
Solksjaer also believes United are on the right track to reach the levels of Liverpool and Manchester City. The Reds recently ended their Premier League drought by winning their first top-flight title in 30 years and end City's hopes of a hat-trick.
"I watched two very good teams on show,' said the United manager. 'We believe we're on the right track, and can improve and close the gap further.
"It's been a while since we've been on a run like this. When I first came in the run was a good one also, but definitely we are feeling confident. The players should be. They worked so hard in the lockdown period," he added.
Silva announced his farewell on Monday in an emotional video message on Chelsea's website
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