A few thoughts about your Project.
You say you would need to sample 14 bits at the sampling rate of 32 MHz. The maximum speed you could obtain with the Arduino DUE is throughout a DMA transfer of 32_bit words.
Let's suppose that the target is to transfer 32_bit words at the pace of 32 MHz = 128 M Bytes /s . But, some questions remain pending:
What would be the length of the recording ??
What do you try exactly to detect in the incoming signal ??
More details on your project could eventually lead to a better understanding, and an Arduino solution. As we know only a very limited part of your overall project, it is extremely difficult to imagine the best trade off with an Arduino board!!.
The DUE has 96 KB contiguous SRAM plus 4 KB SRAM not contiguous, so let's imagine that 10 K 32_bit words would be enough.
If you choose 14 pins of PIOB, and consider transferring the content of PIOB->PIO_PDSR to a buffer, you can achieve this within a memory2memory AHB DMA, although for some reasons, reading the memory PIO->PIO_PDSR is not exactly like reading an SRAM buffer.
Some time ago I did a few tests and achieved a 86 M Bytes /s transfer from PIOB->PIO_PDSR to a 2048 32_bit words buffer. I suspect that this is due to a bus contention somewhere because an SRAM to SRAM memory2memory AHB DMA can be done at the pace of 130 M Bytes /s. I tried to modify the bus Matrix arbitration without much success to overcome this limitation.
Second option : Arduino DUE has an High Speed Multimedia Card Interface (HSMCI) which has its own dedicated DMA programmable through the HSMCI_DMA register. The HSMCI operates at a rate of up to Master Clock divided by 2 (i.e. 84 MHz/2 = 42 MHz) and supports the interfacing of 2 slot(s). Each slot may be used to interface with a High Speed MultiMediaCard bus (up to 30 Cards) or with an SD Memory Card.
I didn't try this feature but it would be the best answer to transfer a very large record, although as already stated in this thread, an SD card introduces some latencies.
Third option : Arduino DUE is 3.3v compliant and you can hook your analog device directly to one of the twelve available analog pins (A0,1,2,3,4,5,6,7,10,11,12,13) of the 12-bit Analog-to-Digital Converter (ADC). In this case, the best you can expect is a pace of MCK / 2/21 = 2 M samples/s within a peripheral to memory PDC DMA.