LTSS IS SUSPECTED BY RPTR IN SPITE OF EFFORTS BY CTLR TO TURN ACFT.

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WE WERE LEVEL AT FL350 (MSP TO ABQ) HDG 230 DEGS. WE WERE GOING DIRECT GCK FROM OMA. WE WERE GIVEN A HDG OF 210 DEGS FOR TFC; THEN HDG OF 160 DEGS FOR TFC. WE HEARD ANOTHER HDG SUDDENLY GIVEN TO AN ACR FLT ALSO AT FL350. AS WE HEARD THIS WE SUSPECTED A CONFLICT AND SHORTLY WERE TOLD TO TURN R TO 240 DEGS AND 'EXPEDITE.' ABOUT HALF WAY THROUGH THE TURN WE OBSERVED ANOTHER ACFT ON TCASII AT 100 FT BELOW OUR ALT. AT ABOUT THE SAME TIME WE OBSERVED THE OTHER ACFT VISUALLY AND COULD SEE THAT OUR COURSES WERE DIVERGING (HE WAS TURNED FROM SW TO S AS WE WERE TURNED FROM S TO SW). OUR ESTIMATE OF MINIMUM CLOSURE WAS ABOUT 4 MI. IT WAS OBVIOUS TO US THAT THE CTLR HAD FORGOTTEN ABOUT US BOTH; HOWEVER; NOTHING WAS SAID TO US; AND WHEN THE ACR FLT MADE AN INQUIRY HE WAS ONLY INFORMED THAT THE SUDDEN HDG CHANGE WAS FOR TFC. HE MAY NOT HAVE EVER SEEN US. THE CTLR DID NOT INDICATE TO US WHY TO EXPEDITE THE TURN OR THAT WE HAD TFC AT OUR 9-11 O'CLOCK POS. THIS DEFINITELY IS AN UNSAFE SIT THAT NEEDS TO BE ADDRESSED.