Guernsey boss Jordan Reynolds says his side are capable of holding on to fifth place in National Three London.
It would be the club's highest ever finish in the English national leagues.
Guernsey's hopes were improved after they beat Tring 33-26 at Footes Lane to move three points clear of sixth-placed Bury St Edmonds.
"A win away to Barnes should cement a top-five spot. If we're sitting around that top five that'll be our highest position," Reynolds told BBC Guernsey.
Blair Campbell, Shane Taylor and Luke Sayer all scored tries for Guernsey, while full-back Sam Whitehead kicked 18 points for the Sarnians.
"It was a hard slog, but we did really well and got the result," Reynolds added.
"Mathematically there's no saying we can't get into that top four. But realistically if the results go our way we'll be in the top five."