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The 23-year-old Scot, who holds five outdoor and indoor British records, ran a personal best four minutes 19.12 seconds over the distance last year.
Budd's mark, set in Switzerland in 1985, is 4:17.57.
"It would be brilliant one month out from the World Championships," Muir told BBC Sport.
"To have another British record, and in the London Stadium again, would be fantastic. Fingers crossed I will be able to do something."
The world record - set by Russian Svetlana Masterkova in 1996 - stands at 4:12.56.
At last year's Anniversary Games, Muir broke the British 1500m record that had stood since Dame Kelly Holmes' gold medal-winning run in the 2004 Olympic final in Athens.
She expects her return to bring back happy memories.
"The main thing was just how loud the crowd was," said Muir.
"I am usually very focused on my race but I was just aware as I came into the final 200m of the crowd getting louder and louder. It was brilliant."
With the Anniversary Games just four weeks before Muir plans to take on a 1500m and 5,000m double at the same venue in the World Championships, it will also be a chance to maximise home advantage.
"It is really really helpful to know where the call-room, the warm-up areas, the kit drop-off and the toilets are," she added.
"Knowing that set-up is one of athletes' biggest worries going into a major championship.
"You want to have everything ready and not have to worry about anything else apart from doing the best you can on the track."
Alongside leading Britain's next generation of elite athletes, Muir is also training to become a vet.
Juggling studying and sport dates back beyond the London 2012 Games, when she organised a placement on a dairy farm so she would finish inspecting the morning milking round in time to watch the Olympic action at home in Kinross.
This year she has already squeezed in experience with the Dogs Trust and various local practices around winning 1500m and 3,000m gold at the European Indoors. The rest of the season is dedicated solely to athletics.
"After the disappointment of finishing seventh in Rio, we knew how important the indoor season was for me in the build-up to London," she added.
"We wanted to do really well there. We ticked that box pretty well and now everything is building towards London."
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The 51-year-old Welshman was only appointed in May, but the club are 16th in the table after Saturday's 4-0 home defeat by Swindon Town.
Saunders lost 11 of his 20 league games in charge, and the Spireites are only four points above the relegation zone.
Chairman Dave Allen said: "We will not be rushed into making a decision on a new manager."
Chesterfield's last league victory was a 3-0 win over Southend on 20 October, and they have lost their last four games.
Saunders succeeded Paul Cook as Spireites manager, signing a two-year contract.
Cook had guided the Derbyshire side to the League One play-offs, where they lost to Preston, before leaving to take over at Portsmouth.
Former Wales international Saunders had previously managed Wrexham, Doncaster Rovers and Wolves, and ended last season in interim charge of Crawley Town, but was unable to stop them being relegated to League Two.
Laura Muir will attempt to break Zola Budd's 32-year-old British mile record at the London Anniversary Games on 9 July.
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League One side Chesterfield have parted company with boss Dean Saunders after just six months in charge.