The telecoms giant announced earlier this month that Patterson would step down later this year after almost five years at the helm.
“BT's admission of a need for change puts Ofcom under pressure to respond constructively,” Jefferies said.
Jefferies raised its rating on BT to ‘buy’ from 'hold' and lifted its target price to 245p from 215p.
The broker said BT’s relationship with regulator Ofcom was strained last year as the company had prioritised dividends over investing in upgrading the UK’s broadband network with fibre optics to improve internet speeds.
But last week Ofcom welcomed BT’s acceleration plans for bringing faster internet connection to three million premises by 2020 and hailed progress with the group’s legal separation from network division Openreach.
“Changing CEO, raising capital expenditure to accommodate new FTTP (fibre to the premises) ambition and trimming dividend per share guide to flat should be sufficient evidence of reordered priorities to facilitate dialogue on a 'fair bet' framework,” Jefferies said.
Jefferies said a dividend cut should not be ruled out as capital expenditure could rise further to support the company’s FTTP plans.
"Ruling out a dividend cut would be unwise," it said.
"Securing the ‘fair bet’ may require a scale of FTTP deployment that forces capex up again, and compels BT to find breathing space."
Shares in BT gained 2.2% to 213.3p in morning trading.