Dyche has been widely heralded for promoting the Clarets to the Premier League on a modest budget??last season and ensuring safety is still possible with four games to go.
The 43-year-old, who joined the club in 2012, has been linked with a number of other jobs but Mee hailed the work his boss has done under difficult circumstances this term.
Mee said: “He has brought a lot of the lads’ games on in his time here so obviously we??definitely want to keep hold of him.
“He has not just taken the selfish route and bought loads of players. He’s??worked with the people upstairs and done really well. It’s been a good couple of years for the club to expand.
“It will be a massive challenge for us but we are looking forward to it – we??still have that belief. The games coming up are massively winnable and we will look to do that,??definitely.”
The Clarets are five points from safety and face an inconsistant West Ham side on Saturday at Upton Park.
And Mee said: “West Ham have had an up-and-down season. They started off really well, now they are flying round mid-table so we will??look to go there and hopefully take advantage of them switching off until the??end of the season.”