The 25-year-old Israel international watched Tuesday's 4-2 friendly win over Blackpool, and Press Association Sport understands the deal should be completed by the weekend once the player has been granted a work permit.
Shechter, who has 13 caps to his name, moved to Kaiserslautern from Hapoel Tel Aviv last summer, but struggled for form in his maiden Bundesliga campaign, scoring just three goals.
The striker will become manager Michael Laudrup's fourth signing after the arrivals of Michu, Jonathan de Guzman and Chico Flores.
Laudrup is hoping to further bolster his squad by adding a winger to his roster, while he has also been linked with a move for Bolton midfielder Mark Davies.
It is understood that the Swans are interested in the 24-year-old although they have not confirmed whether they have lodged a bid.
Davies would be seen in some quarters as a potential replacement for Liverpool target Joe Allen.
Laudrup is set to hold talks with the Wales international over the interest from former boss Brendan Rodgers as the GB Olympic pick returns to training on Wednesday.
Scott Sinclair, who also returns to training on Wednesday, is another to be linked with an exit from the Liberty Stadium.
The winger, who has less than a year left on his contract, is reportedly a target for Premier League champions Manchester City.
- Michael Laudrup
- Hapoel Tel Aviv