Newport and Currie are on the menu in the cup before Worcester return to league action on Boxing Day with a huge local derby against Moseley Rugby.
Warriors will go into the festive league encounter knowing a top eight league place is now a mathematical certainty.
However, Hill insists finishing top of the league table - and not just the first eight - remains a key priority and he plans to use the cup games over the next two weeks to continue to build momentum and form.
"We will keep going until we know we have mathematically finished first," said Hill. "In this league, with the format for stage two, it is important you finish top.
"We are just trying to create a bit more daylight between ourselves and Bedford who keep pushing on, they are on our tails.
"We have just got to keep pushing to get five points each game. We would like to be, with a game or two to go at the end of the season, mathematically sure of being first. We can then review our planning for the play-offs.
"We have got to keep driving the players until the last minute," he added. "Those play offs and semi-final, if you manage to get there, are going to be absolutely crucial.
"You have to get all the little things right and you can't afford to leave anything to chance. The players have to be in absolute superb physical condition, all your skills have to be right and you can't leave anything to chance.
"It is a very interesting coaching dilemma and challenge for players to push on. We have got to be 100 percent come those play offs."
Tickets to watch Warriors face Newport in the British & Irish Cup (December 11) and Moseley Rugby in the RFU Championship (December 26) are available now from the Warriors Box Office. Call 01905 454183 for more information or click HERE