The Swede, who arrived on a free over the summer, has claimed 28 goals in all competitions so far this season under Jose Mourinho.
Doubt remains over whether Zlatan, now 35, will elect to sign an extension on his contract that stretches his Man United career into 2018.
Shaw, speaking soon after United’s 3-0 win over Sunderland, a game in which Zlatan grabbed a goal and an assist, made it clear that the 35-year-old was vital to the side’s approach.
“Listen, whatever he says he backs up,” he chuckled. “He always delivers and he delivers at the most important times.
“At Sunderland he was really good again, setting up [Marcus] Rashford’s goal at the end and obviously scoring the important goal for us at the start.
“It is wonderful to have a great player like him in our team and hopefully he keeps going until the end of the season and helping us.”
Out of anybody in this United squad it is perhaps Shaw who could learn the most from Zlatan. The Swede does more than just occupy the No.9 role for Mourinho; he also sets a standard – a psychological benchmark that demands not just a winning mentality but an insatiable desire to demolish anything that comes in the opposite direction.
Can you imagine Zlatan, like Shaw did back in November, pulling out of the squad on the morning of a game as a result of mental and physical fatigue? Such an idea is actually laughable.
United fans will hope that Shaw, as he plays for his career under Mourinho, imbibes the spirit of his side’s Swedish hero over the next month.