The Magpies remain in talks with the Ligue 1 club over a deal to bring the highly-rated Dutch Under-21 international to St James Park.
United’s interest in Botman is longstanding and they made several unsuccessful attempts to conclude a deal during the January transfer window.
Despite their best efforts, the 22-year-old remained with Lille but always seemed open to a move away from the French club during the summer transfer window.
United are not the only club to shown an interest in Botman with Serie A giants AC Milan also keen to take the centre-back to Italy.
Reports have suggested delays caused by a protracted takeover bid by US-based private equity firm RedBird Capital Partners is hampering Milan’s attempts and leaving the door open for Newcastle to secure one of their long-term transfer targets.
There have been conflicting reports over Botman’s interest in a move to St James Park - but Woodgate insisted his former club would ‘up the ante’ in their defensive ranks if the Dutchman does arrive during the summer transfer window.
He told BBC Five Live: “It really would strengthen their defensive line.
“To be fair, since Eddie Howe and Jason Tindall have come in, they have improved that defensive line.
“The signing of Dan Burn, Trippier and Matt Targett at left-back. They really have improved. And Fabian Schar, who had a really great end to the season.
“Sven Botman would really up the ante. He’s a really good player. He’s a top player.”
Botman is not the only defender on United’s list of targets but it does seem the Magpies will continue with their efforts to conclude a deal for the centre-back over the coming weeks.