The GFS is showing a pretty sloppy upper air pattern over the next seven days. The only potential chase opportunity will be this coming Friday when a positively tilted trough approaches the central/southern plains.

A closed low is going to move through the far southern plain part of Texas on Monday and then push off to the east coast by midweek.
On Thursday a strong jet streak will move out of the Pacific Northwest and into the back side of a small trough along the Canadian border. This will increase the amplitude and dig the trough farther south Thursday into Friday. At the same time a jet streak in the sub-tropical jet will move east through zonal flow and enter the plains at the same time as the trough in the polar front jet.
Northerly low level winds through midweek will shun moisture southward and prevent any quality moisture from being advected back into the plains when the low level flow does switch to southerly with the approach of the upper level trough. The GFS is currently showing dewpoints in the lower 50′s across the warm sector on Friday. I haven’t spent any time on details yet, so I have no opinion on whether or not that seems realistic.
It is too far out to get into details, but the GFS is showing good wind shear at all levels and if storms can break the cap we have a decent shot at severe weather. Any possibility of tornadoes is probably going to depend a lot on moisture quality and instability.
I will keep any eye on this and update the forecast tomorrow or Tuesday. Hopefully things will be a little more clear by then. I should be able to get some idea of the moisture situation by Tuesday-Wednesday.