Is it possible to interface 89C52 with 23s17 (port Expander), If it is possible means whether interfacing through TXD and RXD is good or using General purpose Port pins for SPI
You can't use UART for SPI. A software SPI, using any 4 available port pins will work. Using an I2C port expander could reduce the pin count to 2, but needs slightly complexer software.
Pins are SCK, SDO(MOSI), SDI(MISO) and chip select (SS). All signals are generated by software (so called bit-banging). There are plenty of examples on the internet.