Bjorkman joined Amelie Mauresmo on Murray’s coaching team in April, with a remit to help the British No 1 improve his net-play and instil a more attacking strategy.
Mauresmo is currently on maternity leave, meaning Murray will be without his main coach in New York for the first grand slam in over a year, and leaving Bjorkman to step into the role of principal confidant.
Initially brought in for a trial period, the Swede’s energy and enthusiasm proved an instant hit in Murray’s set-up, but the Scot admits it has taken time for deeper connections to develop.
“He’s a very positive guy. He’s very calm. He came into the team with no ego at all,” said Murray.
“He wanted to learn and understand how we worked. He has asked a lot of questions so he could get to understand me better.
“I feel the last few weeks have been really, really positive because it takes time to develop a working relationship.
“It takes time for me to open up and tell someone how I am feeling.
“He’s just been very positive. He’s a hard worker. When he played, his game style was very much based on net play, returning – so he’s able to help me with a lot of things.”
As well as honing Murray’s more creative talents, Bjorkman is often the Scot’s sparring partner in practice, reviving his former competitive instincts as he tries to push his pupil in points.
“Is he as competitive as me? I’d say so. He’s a pretty competitive guy,” Murray said.
“He’s got a pretty bad temper as well. I’d say my temper is not as bad in practice as it in matches – but he’s got a worse temper than me on the tennis court away from camera I’d say.”
Murray has been handed a tough opening round against Nick Kyrgios tomorrow, but success at Flushing Meadows will likely mean overcoming Novak Djokovic, the outstanding player in the world this season and against whom two of the Briton’s three major tournaments have ended this year.
A miserable run of eight straight defeats against the Serb finally came to an end in Montreal last month, when Murray ousted the world No 1 in three close sets.
“It was a big win for me for a bunch of reasons,” Murray said.
“After Washington (where Murray lost in the second round), to come back and win the tournament there was big and also against Novak, coming back and being very strong in the third set.
“A couple of times this year, the final sets of matches have got away from me. That could have happened again in Montreal but I stayed strong and got a big win there.
“It’s important for me and important for me to get that confidence ahead of the US Open.”
Murray, seeded third, played first-round opponent Kyrgios at both the Australian Open and French Open earlier this year, winning on both occasions without dropping a set.
The British No 1 is bidding to clinch his third grand slam title and regain the crown he won at Flushing Meadows in 2012.
It represents a tough opening draw for Murray, who was placed in the same half as Federer and could also face French Open champion Stan Wawrinka in the quarter-finals.
The Scot will first, however, have to overcome the unpredictable Kyrgios, who has endured an explosive year on and off the court.
Kyrgios was handed a suspended 28-day ban and $25,000 fine last Monday for disparaging comments made towards Wawrinka about his girlfriend at the Rogers Cup in Montreal earlier this month.
There were also suggestions at Wimbledon that the 20-year-old stopped trying during his fourth-round defeat to France’s Richard Gasquet.
Murray has been a loyal defender of Kyrgios’s antics, insisting after the altercation with Wawrinka that he is “not a bad guy” and is “growing up in the spotlight”.
When the Australian is firing on all cylinders, he is one of the game’s most talented prospects, demonstrated by wins over Federer in May and most famously Rafael Nadal at Wimbledon last year.
Victory over the controversial world No 37 would see Murray play either Adrian Mannarino or a qualifier in the second round, and he could then meet fellow Briton James Ward in round three.
Ward opens up against Brazil’s Thomaz Bellucci while British No 2 Aljaz Bedene has been drawn against Latvian Ernests Gulbis.