B737-700 FLT CREW DISCOVERS A RODENT ON THE ACFT.

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UPON ARR AT ACFT ON ORIGINATOR OUT OF ISP; FOUND SOME RUBBER SHREDS ON THE FLOOR NEXT TO COCKPIT DOOR. DETERMINED THAT THE SHREDS WERE MOST LIKELY FROM THE RUBBER WX SEAL AT THE BOTTOM OF THE COCKPIT DOOR. ALSO NOTED THAT THE RUBBER SHREDS LOOKED LIKE THEY MIGHT HAVE BEEN THE RESULT OF A RODENT CHEWING ON THE WX SEAL. PERFORMED A VISUAL INSPECTION OF THE AREA AND SAW NO OTHER INDICATIONS OF ANY ANIMALS AND PROCEEDED WITH NORMAL OPS. AT THE END OF THE SECOND FLT ON DSCNT INTO BWI; THE FLT ATTENDANTS FOUND A RAT ON THE FLOOR NEAR THE FORWARD FLT ATTENDANT JUMPSEAT. THEY COULD NOT DETERMINE WHERE IT CAME FROM. IT APPEARED TO BE 'GROGGY' AND THEY KICKED IT TO THE SIDE BY THE FORWARD ENTRY DOOR AND KICKED IT OFF THE AIRPLANE WHEN WE PARKED AT THE GATE. AFTER CONSULTING WITH MAINT CTL THE ACFT WAS TAKEN OTS FOR FURTHER INSPECTION. IN RETROSPECT; I SHOULD HAVE CONSULTED WITH DISPATCH AND MAINT UPON ARR IN ISP TO DETERMINE IF THERE WERE ANY ISSUES RELATED TO THE WX SEAL AND POSSIBILITY OF A RODENT ON THE ACFT.