DAL GND CTLR DESCRIBED SEPARATION EVENT; 4500 FT; INVOLVING ARR TO RWY 13R AND DEP FROM SAME RWY.

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I WAS WORKING GND CTL AT DALLAS LOVE ATCT. I SAW THE FOLLOWING: I JUST GOT DONE GIVING TAXI INSTRUCTIONS TO AN ACFT AND IDENTING HIS POS WHEN I LOOK AT THE APCH END OF RWY 13R AND SAW AN ARRIVING B737 PASSING TXWY C6. I SAW THE TRAINEE AND THE TRAINER ON LCL CTL LOOKING TOWARD THE DEP END. WHEN I SCANNED TOWARDS THE DEP END OF RWY 13R; I SAW A B737 ABOUT TO PASS TXWY C3 WHICH APPEARED TO HAVE HIS MAIN GEAR STILL ON THE RWY. LCL CTL DID NOT INFORM THE OPS SUPVR OF THE POSSIBLE OPERROR. I GOT OFF GND CTL ABOUT 10 MINS BEFORE THE END OF MY SHIFT. I DID NOT HAVE THE OPPORTUNITY TO TALK WITH THE LCL CTLR ABOUT THE SIT UNTIL I WAS ON MY WAY HOME. VIA TELEPHONE; I INFORMED THE LCL CTLR THAT HE HAD TO RPT THE POTENTIAL OPERROR WITHIN 3 HRS. HE SAID HE WOULD DISCUSS IT WITH THE CURRENTS OPS SUPVR. I CALL MY OPS SUPVR ABOUT THE SIT. HE CALLED THE FACILITY AND WAS TOLD BY THE OPS SUPVR ON THE SHIFT THAT THE SIT WAS BEING INVESTIGATED. I WAS NEVER CONTACTED ABOUT WHAT I SAW. I WAS TOLD THAT THE SIT WAS CONSIDERED A NON-EVENT.