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The 16-year-old beat Anne Keothavong's record as the youngest British player to play in the Fed Cup in February.
Swan won her first two titles on the second-tier ITF tour in 2015, and made her WTA debut at Birmingham in June.
"There's a few big grass tournaments before Wimbledon so I'm hoping I get to play in some of them, whether it's qualifying or main draw," she said.
"There's a chance I might get a Wimbledon main draw wildcard, but I'm not sure about that yet.
"Definitely I'll keep working towards that and it'll be amazing if I can make my Grand Slam debut this year."
Swan also said she hopes to improve her results in Junior Grand Slam tournaments in 2016.
The Bristol-born player is ranked number 12 in the world at junior level, and reached the final of the Australian Open junior tournament in 2015.
"My goal this year in juniors is to try to do really well in the Grand Slams. I'd like to aim to win a Grand Slam, which would obviously be amazing for me," she continued.
"On the women's tour, I just want to keep working on my ranking and try to do the best I can in all those tournaments, and maybe be able to get into qualifying for the Australian Open next year."

Parts of Madeira Terraces, have been fenced off since summer after warnings the Victorian structure could collapse.
Council leader Warren Morgan revealed in a Facebook post the authority has applied for Â£50,000 from the government's coastal revival fund.
Homeless people had been sleeping under the arches.
Mr Morgan said: "It is the preliminary step of the restoration process and whilst it does not detail our plans, I hope that it shows that a process, however slow, is underway."
The concern with the structure surrounds the corrosion of steel beams embedded in concrete which supports the deck of the terraces.
It was announced in October that more fencing was to be installed after rough sleepers were discovered.
At the time, Mr Morgan said the site would be secured and staff would help people find safer accommodation.
British world number 512 Katie Swan says she hopes to earn a wildcard entry into the main Wimbledon draw this year.
[NEXT_CONCEPT]
Brighton's crumbling seafront arches may be restored after the council revealed it has applied for funding to help redevelop the site.