McDavid, 20, selected by the Oilers one spot ahead of Eichel in the 2015 draft, signed an eight-year, $100 million contract extension ($12.5 million average annual value) on July 5 that begins next season. Johansen, 25, signed an eight-year, $64 million contract ($8 million AAV) with the Predators as a restricted free agent July 28. Draisaitl, 21, signed an eight-year, $68 million contract ($8.5 million AAV) with the Oilers as a restricted free agent Aug. 16.
Eichel would become a restricted free agent on July 1.
"It's an important deal for the organization and an important deal for Jack," Botterill said. "I will say is that I still think the conversations are very cordial and very positive, and when you have both parties wanting to get a deal done, I do believe eventually a deal will get done."
Eichel, who turns 21 on Oct. 28, has 113 points (48 goals, 65 assists) in 142 regular-season NHL games. Last season, after recovering from a high ankle sprain that kept him out for the first 21 games, he had 57 points (24 goals, 33 assists) in 61 games.
The Sabres went 33-37-12 (78 points) and finished 15th in the Eastern Conference last season after going 35-36-11 (81 points), 14th in the East, in 2015-16.
Eichel will try to help the Sabres reach the Stanley Cup Playoffs for the first time since 2010-11. Last season led to the firing of GM Tim Murray, replaced by Botterill, and coach Dan Bylsma, replaced by Phil Housley.
Botterill also said there is no rush to naming a captain prior to the start of the regular-season opener against the Montreal Candiens at KeyBank Center on Oct. 5.