Positioning of nucleosomes along the genomic DNA is crucial for many cellular processes that include gene regulation and higher order packaging of chromatin. The question of how nucleosome-positioning information from a parent chromatin gets transferred to the daughter chromatin is highly intriguing. Accounting for experimentally known coupling between replisome movement and nucleosome dynamics, we propose a model that can obtain de novo nucleosome assembly similar to what is observed in recent experiments. Simulating nucleosome dynamics during replication, we argue that short pausing of the replication fork, associated with nucleosome disassembly, can be a event crucial for communicating nucleosome positioning information from parent to daughter. We show that the interplay of timescales between nucleosome disassembly (tau (p)) at the replication fork and nucleosome sliding behind the fork (tau (s)) can give rise to a rich 'phase diagram' having different inherited patterns of nucleosome organization. Our model predicts that only when tau(p) >= tau(s) the daughter chromatin can inherit nucleosome positioning of the parent.