Easy enough to implement master functionality with a few more logic chips. Few latches, small counter, comparators -- make a basic state machine to control a shift register, and the clock (making sure the clock enable is synchronous with the clock, and adapting clock domains if the clock is independent from the bus) and chip select signals. Interrupt can simply be gated from CS rising, or something like that.
I'm not sure what use there is in integrating all that? SPI is ubiquitous in MCUs, parallel buses are uncommon. Certainly there's no point today. Perhaps there would've been a brief period in the 90s, when parallel buses (MPUs) were still popular, and SPI peripherals were increasingly popular. Seems like that would be your best bet, looking for something long-obsolete that you can get some spares of.
There is the old fashioned UART (in chip form), which has offered similar functionality for decades. Specifically you'll need a USART type, using the "SRT" set of functions. I'm not sure offhand that a classic 8250 or 16550 has that functionality, but there's probably something out there. Every family had their own thing (Intel 8250, Motorola something, Zilog Z80-SIO, etc.), I don't know what differentiates them. Shop around. Again, to the extent that you can shop among probably-obsolete parts. Maybe look up old catalogs (Digi-Key, Jameco, etc.) and data books.
Edit: ah, I see my historical insight was correct!
Tim