There is no relationship between SWR and receive performance.
There is one condition for this simplification to be true: the received RF noise floor must be above your receiver's noise floor. Beyond this, anything you might do to increase the output from the antenna does nothing to increase the signal to noise ratio, which is a better measure of receive performance.
SWR is a measure of the impedance mismatch between your antenna and transceiver. Whether transmitting or receiving, a higher SWR correlates with a less efficient coupling of energy between the transceiver and antenna.
This inefficiency is problematic when transmitting because it can make a lot of heat, and it limits one's ability to overcome noise at the intended receiver. We could compensate with an amplifier, but high-power amplifiers are expensive, and big, and hot, etc. However when receiving, losses are easy to overcome. The heat generated is insignificant, and at the extremely low power levels involved in receiving, amplifiers are not large or expensive or difficult to design.
Remember also that losses attenuate the signal, and also the noise equally. Improving the SWR will increase the power received, but this is signal and noise, and thus does nothing to make the signal more intelligible, unless both are attenuated so much that most of the noise is no longer coming from the antenna, but instead from the electronics of the receiver. At HF, low-noise amplifiers are easy to design, and the ambient RF noise floor is relatively high, so antenna efficiency (including SWR-related losses) is not usually the limiting factor in receive performance.
If you want a wide-band antenna for receiving, then you may do well with a non-resonant antenna. Such an antenna will be very inefficient, but this easily compensated with a low-noise amplifier. Because it is not operated at resonant frequencies, bandwidth is hardly a concern. A small loop or its electrical dual, the Hertzian dipole could work. Or, consider a Beverage antenna if you want directionality, which does increase signal-to-noise ratio, provided it's pointing in the right direction.