But not even the persuasive skills of Gunners and Lionesses great Alex Scott could convince Girma to change her mind.
The Blues announced the capture of Girma from NWSL outfit San Diego Wave for a reported $1.1million (£881,000) on Sunday, making the American the first female player to be signed for a seven-figure fee.
But in another world, Girma could have moved to the Emirates Stadium instead as Scott jokingly asked the 24-year-old where she went wrong in her sales pitch.
"I'm just asking for a friend here, because like I mentioned, there were a number of teams after you," Scott said on BBC Sport.
"Arsenal sent me along to the directors' box to try and help you be a Red, but it didn't turn out. So I just need some feedback."
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Girma laughed and replied: "You were amazing."
The California native sat in the stands at Stamford Bridge to take in Chelsea's 1-0 win over Arsenal on Sunday in the WSL, with the result perhaps offering some sense of justification for her choice.
Guro Reiten's penalty in the 84th minute was all that separated the two sides.
The Blues were awarded a spot kick when Kim Little tripped up Lauren James inside the box.
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A host of Arsenal's stars protested the decision but Katie McCabe appeared to overstep the mark as she was shown a second yellow in the aftermath.
However, it was Girma who was the star of the afternoon.
She was paraded around the stadium prior to kick-off as Blues supporters offered their well wishes.
The move marked Girma's first overseas adventure as a player having been selected by the Wave with the first pick in the 2022 NWSL Draft.
She helped the team win the NWSL Shield in 2023 and went on to be named US Soccer's female player of the year.
Girma also played a starring role in helping the USWNT win a gold medal at the Paris Olympics, snapping the nation's 12-year wait for another first-place finish at the Games.
So impressive was Girma, former Chelsea Women's and current USWNT boss Emma Hayes labelled her 'the best defender I've ever seen.'
"I've never seen a player as good as her at the back," Hayes said.
"She's got everything. Poise, composure, she can defend, she anticipates, she leads. [She's] unbelievable."
Girma's addition provides some much-needed defensive reinforcement for Chelsea as Kadeisha Buchanan remains sidelined with an ACL injury.
The American is also a strong chance of winning the WSL in her first season as Chelsea's win over Arsenal gave them a seven-point lead at the top of the table.
Sonia Bompastor's side sit on 34 points, with Manchester United in second on 27.
As for Arsenal, they are fourth on 24 points following the defeat.