We will evaluate available information one by one and try to reach some conclusion
A- Sources mentioning about Nalanda (of Pavarika & University) and Birthplace of Sariputra in one context
• There are two strong contemporary references which speak about Nalanda and birth place of Sariputra in same breath and yet maintain it to be different places. The first and the major source of evidence are the Pali sources which are the record of events and place associated with Buddha and his disciples.
To reach any conclusion we need to know more about what other old texts says about places. We have a detail history of places and events around Rajgriha at the time of Buddha which are very well maintained in the Pali traditions. The Pali proper name dictionary is compilation of all the places mentioned in Pali sources.
Nalanda- A town near Rajgriha and according to Buddhaghosa one league away
Nalanda finds mention in Digh Nikaya, page 35, Kevatta sutta, Majhima Nikaya etc
As per the Kevatta sutta Nalanda was an influential and prosperous place
Some Pali sources maintain that Nalanda was 1 Yojan from Rajgriha and Pavarika mango grove was a part of it.
Nala/ Nalaka /Nalika
A Brahmin village in Magadha not far from Rajgriha. It was here where Sariputra was born. Mahasudassana-Jataka also mention Nala birth place of Sariputra
Pali sources and the Pali Tripitaka are the contemporary accounts as far as Buddha and Sariputra are concerned. This was orally maintained for centuries before it was first written in Singhalese script in Srilanka. Whole of the Pali sources available till date uniformly maintains Nala (Nalaka & Nalika) as the birth place of Sariputra. And there is no single instance of Nalanda and Nala being mentioned as same. Pali sources have been preserved by Theravada sect who is traditionally believed to preserve the Words of Buddha Verbatim.
• Travelogues of Xuanzang who visited both the places in 7th century, maintains it to be two different places. There are chances that Nalanda of Pali reference and Nalanda of University have some connection but the Nalanda of University and birth place of sariputra are two different places.
These two evidences establish that Nalanda Monastery and Nalanda of Pavarika mango grove are different from the birth place of Sariputra. Yet there are no clues that would suggest a correlation between Nalanda monastery and Nalanda of Pavarika mango grove.
Also it does not negate another possibility of a monastery named Nalanda at Nala, the birth place of Sariputra.
And since we are on the topic of discussing sariputra and the monastery named after him, the guides at Nalanda ruins mention the temple no. 3 as Sariputra Chatiya when it is evident from Xuanzang’s travelogue that it is related to the Buddha himself.