B737-700 Captain reported abnormal airspeed indications on the MFD speed tape display. Flight crew diverted and landed uneventfully.

Narrative

We were on an international flight from ZZZZ to ZZZ1. During configuration for landing at ZZZ1 - FO (First Officer) was pilot flying - we noticed the speed tapes on the MFD's (Multi-Function Flight Display) were showing abnormal indications. With landing gear down; flaps 25; and engine anti-ice on the flaps 25; speed bug was in the yellow band and flaps 40 VREF was in the red band. Unsure of our situation we elected to accomplish a go-around and requested vectors for a holding pattern to evaluate. I quickly talked to the flight attendants and informed them we had an anomaly we were trying to figure out. The flight attendants made a quick PA to inform the passengers. We resubmitted our performance data; landing data; and made sure everything was submitted correctly; including landing weight and engine anti-ice. The landing data that came back looked right and the speeds matched the FMC speeds at that time. Our gas was at 5.6 and we decided we needed a longer runway for a flaps 15 approach; since flaps 40 VREF was in the red band earlier. We elected to divert to ZZZ. I quickly informed Dispatch and the flight attendants. Flight attendants informed the passengers. We were vectored for a flaps 15 approach to Runway XXC at ZZZ. We resubmitted our performance data landing data and noticed that performance data flaps 15 speed was 146 while FMC generated speed was 135. We obviously elected to go with the faster speed. I took the aircraft for landing. Once configured for a flaps 15 landing our flaps 15 VREF speed of 146 was two kt. above the yellow band and 17 kt. above the red band. I elected to fly a couple kt. faster so as not to land with the speed in the yellow band. We touched down about five kt. above the yellow band. We landed uneventfully and taxied to Gate XX. The FO made a nice face-to-face PA with the passengers summarizing what happened while I initiated a call with Dispatch. We had a 5-way conversion with Dispatch; Chief Pilot; Maintenance; and some sort of Regional Manager. I wrote up the anomaly with coordination with Maintenance and Contract Maintenance arrived at the aircraft and starting coordinating with our Maintenance. All passengers and crew exited and went through Customs.Since no assistance was needed upon landing at ZZZ and at the time our landing fuel was above 4.0; we elected to not declare an emergency. Upon hindsight and reevaluating our stressful situation; I think declaring an emergency might have been a better decision.[Suggestions are] unknown since we really don't know what happened with our airspeed display. We just tried to take the safest course of action to land the aircraft given we didn't have enough fuel to try another attempt.