Steve Clarke is hoping to keep Glenn Murray at Reading after his loan deal expired following the 2-1 win over Norwich.
QPR boss Harry Redknapp admitted he needs to strengthen his squad after his side's 0-0 draw with Crystal Palace.
Dawson was released after 10 years at the club and subsequently joined former side Scunthorpe.
The Iron have a League Two fixture at Bristol Rovers on the same date as the Betis match, August 10, but Dawson has been given permission to play in his own testimonial instead.
The 34-year-old played 317 times for Hull and was part of four promotion-winning sides.