The 22-year-old was in impressive form for his German club during the 2021-22 campaign, scoring 17 goals and registering 14 assists in 42 appearances in all competitions.
According to Sky Sports News, the Magpies are keen to bring Diaby to the Premier League this summer, but the two teams are currently some way apart in terms of their valuations.
A separate report from 90min has claimed that Eddie Howe's side are prepared to break their transfer record for the France international, with the club willing to pay in excess of £40m.
Elsewhere, Crystal Palace are reportedly closing in on the signing of Flynn Downes from Swansea City.
The 23-year-old was an important player for Swansea during the 2021-22 campaign, making 39 appearances in all competitions, contributing one goal and two assists in the process.
According to WalesOnline, Palace are nearing an agreement with the Welsh outfit over the signing of the midfielder, who has also been linked with Southampton and Wolverhampton Wanderers.
Downes still has three years left to run on his contract with Swansea, placing the club in a strong position to negotiate a high transfer fee for him in the current market.
Meanwhile, according to The Sun, Nottingham Forest are preparing a £10m offer for Huddersfield Town midfielder Lewis O'Brien.
The 23-year-old is believed to be admired by Leeds United, with the Whites viewing him as a possible replacement for Kalvin Phillips, who has moved to Manchester City.
However, it is being reported that Forest are in pole position to sign O'Brien, with the newly-promoted outfit lining up a £10m bid for his services.
The Englishman has made 131 appearances for Huddersfield in all competitions, contributing eight goals and 10 assists in the process.
Forest are also allegedly keen to bring Bayern Munich defender Omar Richards to the club before the end of the summer transfer window.
The 24-year-old joined Bayern from Reading last May, and he made 17 appearances for the Bundesliga champions during the 2021-22 campaign.
According to the Daily Mail, the German giants would be open to selling Richards for around £10m this summer, which has attracted the attention of Forest.
The Reds have already been busy during this summer's transfer window, as they prepare for life back in the Premier League, but head coach Steve Cooper is believed to be keen to land Richards, who made 104 appearances for Reading before moving to Allianz Arena.