Five wins and a draw in their last six matches have moved Frankfurt up to fourth in the table, five points clear of their hosts tomorrow.
"We are delighted that our work is now being rewarded," Skibbe said. "But what pleases us the most is that the others in the league all respect us and take us seriously as a rival.
"Bremen will be highly motivated and concentrated, just like us.
"I hope that we can get at least a point there."
In stark contrast to Frankfurt's form, Bremen have not won in four matches and coach Thomas Schaaf, who has been in charge for 12 years, is under pressure.
"Of course I am unhappy - we all wanted to experience something different," he said.
"We should be getting better results with this team."
After a humiliating 6-0 defeat to Stuttgart last Sunday, Schaaf would settle for an improved performance against Frankfurt.
"We have got to be more compact and stand up for ourselves," he said. "We have got to be able to see that the players want to win, that they want to be defiant.
"We have got to see that we want to be successful."
Schaaf will be without top goalscorer Claudio Pizarro, who could miss the rest of the year due to torn muscle fibres while Hugo Almeida is also a doubt because of a cold.
Skibbe has already announced that he is unlikely to make any changes.