Hearts and Hibs have made contact with Kilmarnock over the availability of striker Steven Naismith.
BBC Sport says the two Edinburgh clubs have stepped up their interest.
But Rangers remain the 20-year-old's favoured club and he might reject a proposed move to any of their rivals.
The Ibrox club have been chasing Naismith all summer, having four bids rejected before withdrawing their final offer of £1.5m.
Kilmarnock are thought to want upwards of £1.7m.