Winger Chris Brunt has been linked with move to Liverpool in January
Roberto Di Matteo's side have shocked a number of teams since they were automatically promoted from the Championship last season, but Scharner insists that their good form can only continue if they stick together as a unit.
The Austrian international said: "It's true we have exceeded expectations but I am very happy that we surprised everybody.
"Hopefully we can continue what we are doing.
"Hopefully we won't stop when we reach our target [of staying up] and we will keep on going until the end of the season.
"It looks like we can stay up. I never got relegated with Wigan and that's why I came to West Bromwich, to help them survive.
"That's the main target and we're on course at the moment.
"But, if we want to reach our targets, it is important that we all stay together until the end of the season."
Baggies boss Roberto Di Matteo has already admitted that he cannot make any big money signings in the coming January window.