Exhibit (a)(1)(vi)

Tender Offer Instructions for Golub Capital Private Income Fund I– June 2026 Quarterly Tender Offer

The below instructions are intended for investors who are seeking to tender their Golub Capital Private Income Fund I (the “Fund”) shares. If you are not interested in selling your shares of beneficial interest in the Fund (“Shares”) for repurchase at this time, please disregard this notice and take no action.

Please note that, except as disclosed in the Fund’s public filings with the Securities and Exchange Commission under the Exchange Act of 1934, as amended, all Shares that have been issued after July 1, 2025 will be subject to an “early repurchase deduction”, which will reduce your proceeds by 2%. Shares that are issued pursuant to the Fund’s distribution reinvestment plan and tendered will not be subject to the early repurchase deduction. In addition, the sale of Shares may also be subject to income and transfer taxes.

The tender offer period will begin on June 29, 2026 and end at 11:59 p.m., Eastern Time, on July 29, 2026 (the “Expiration Date”). The purpose of the tender offer is to provide liquidity to shareholders of the Fund. Shares may be presented to the Fund for repurchase only by tendering them during one of the Fund’s announced tender offers.

Tender Offer Documents

	Ø	Investors should receive notification of the tender offer on or around June 29, 2026.

	Ø	Should you wish to tender all or some of your Shares during this tender offer period, you are required to complete the Letter of Transmittal sent to you and return it as required. If your shares are held at your financial advisor, broker, dealer or other financial intermediary (“Authorized Intermediary”), please ask your Authorized Intermediary sufficiently in advance of the Expiration Date to submit a repurchase request for you. You may be charged a transaction fee by your Authorized Intermediary for this service. Note that certain Shareholders may be required to deliver their Letter of Transmittal to their Authorized Intermediary for the repurchase request to be considered in good order. However, such Shareholders should submit their Letter of Transmittal to the Fund at the same time they submit the Letter of Transmittal to their Authorized Intermediary. Additionally, for accounts held through a custodial relationship, Shareholders should send the completed Letter of Transmittal to such custodian (along with any custodian required documentation) at the same time the Letter of Transmittal is submitted to the Fund. All Shareholders tendering Shares should carefully review their Letter of Transmittal and follow the delivery instructions therein.

If you have any questions, please refer to the Offer to Purchase document sent to you, which contains additional important information about the repurchase offer, or call (833) 327-4024.

Submission of Tender Offer Documents

	Ø	Please complete the Letter of Transmittal and return it by mail or email to the Transfer Agent, Attention: Golub Capital Private Income Fund I, using one of the below options or to your financial advisor as instructed in the Letter of Transmittal.

All tenders of Shares must be received in good order by the Transfer Agent by 11:59 p.m., Eastern Time, on July 29, 2026.

Email

Email address: IC@golubcapital.com and golubcapital@ultimusfundsolutions.com (Please send email to both addresses)

Should you have any questions regarding your submission, please contact IC@golubcapital.com.

There are limitations to how files can be received electronically by the golubcapital@ultimusfundsolutions.com mailbox that are outlined below.

Encrypted emails and .zip files cannot be accepted

Password protected documents cannot be accepted

Emails cannot exceed 35MB

Multiple tenders must be submitted individually

Overnight Mail

225 Pictoria Dr., Suite 450

Cincinnati, OH 45246

Regular Mail

P.O. Box 46707

Cincinnati, OH 45246-0707