Holland and Jenkins' compatriot Stanford pre-qualified for the team in 2015, leaving one more place to fill.
The likelihood is whoever finishes first out of Jenkins, 31, and Jody Stimpson in the World Triathlon race on Australia's Gold Coast will be picked.
"I would love to qualify for another Olympics and go to Rio," said Jenkins.
The two-time former World Champion finished third behind Stimpson in the opening round in Abu Dhabi on 5 March.
"I was happy to come away with a third in Abu Dhabi," Jenkins told BBC Wales Sport.
"I'd had a chest infection and came off antibiotics on the Monday and raced on the Saturday."
The GB team will be announced before the Columbia Threadneedle World Triathlon Leeds, 11-12 June.
British Triathlon say the quality of the performance in Gold Coast will be taken into consideration as well as the finishing positions.
The Welsh athlete would need to finish ahead of Stimpson and show Olympic medal-winning potential.
Jenkins won the world title in 2008 and 2011, and represented Team GB at two Olympic games.
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"I've been to Beijing and London," she said.
"Qualifying means a lot, but it's not going to kill me if I don't go, I'm a lot more balanced coming in to this Olympic cycle.
"I have a massive desire to go, but have balance in my life so if I don't go I have other things I want to concentrate on."
Jenkins has been in Australia for three weeks preparing for this weekend's race.
"I think my fitness has come on really well since I've been here," she added.
"I've had a really decent, consistent block of training and got some more harder running done on the road, which I haven't really done up until this point. I'm feeling strong in all disciplines."
It makes a change for Jenkins who has been plagued with injuries in recent seasons.
"I'm not going to lie, there's been a few times when it's nearly been it and I've thought I just can't do this any more . . . there's been tears," said Jenkins.
"But there's always something that keeps me going. I don't know what it is - but there is something that keeps you going."
See Helen Jenkins' interview on Sport Wales, BBC Two Wales, 19:30 BST on Friday, 8 April.
Welsh athlete Helen Jenkins is determined to join Non Stanford and Vicky Holland in the GB triathlon team at the Rio Olympics.